General information
Latest issue
Impact factor
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Uspekhi Mat. Nauk:

Personal entry:
Save password
Forgotten password?

Uspekhi Mat. Nauk, 2000, Volume 55, Issue 3(333), Pages 103–162 (Mi umn292)  

This article is cited in 289 scientific papers (total in 289 papers)

Metric regularity and subdifferential calculus

A. D. Ioffe

Technion – Israel Institute of Technology

Abstract: The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces.


Full text: PDF file (552 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2000, 55:3, 501–558

Bibliographic databases:

UDC: 517
MSC: Primary 49J52, 58C20; Secondary 58C06, 58E05, 49J53, 46G05, 46A30, 54C60, 49J50
Received: 26.01.2000

Citation: A. D. Ioffe, “Metric regularity and subdifferential calculus”, Uspekhi Mat. Nauk, 55:3(333) (2000), 103–162; Russian Math. Surveys, 55:3 (2000), 501–558

Citation in format AMSBIB
\by A.~D.~Ioffe
\paper Metric regularity and subdifferential calculus
\jour Uspekhi Mat. Nauk
\yr 2000
\vol 55
\issue 3(333)
\pages 103--162
\jour Russian Math. Surveys
\yr 2000
\vol 55
\issue 3
\pages 501--558

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ioffe A.D., “Variational analysis and mathematical economics 2: Nonsmooth regular economies”, Advances in Mathematical Economics, 14, 17–38  crossref  mathscinet  zmath  isi
    2. Dontchev, AL, “Ample parameterization of variational inclusions”, SIAM Journal on Optimization, 12:1 (2001), 170  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Ioffe A.D., “On perturbation stability of metric regularity”, Set-Valued Anal., 9:1-2 (2001), 101–109  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Rolewicz, S, “On alpha(center dot)-monotone multifunctions and differentiability of strongly alpha(center dot)-paraconvex functions”, Control and Cybernetics, 31:3 (2002), 601  mathscinet  zmath  isi
    5. Ioffe A.D., “On robustness of the regularity property of maps”, Control Cybern., 32:3 (2003), 543–554  mathscinet  zmath  isi
    6. Zolezzi T., “Condition number theorems in optimization”, SIAM J. Optim., 14:2 (2003), 507–516  crossref  mathscinet  zmath  isi  scopus
    7. Borwein J.M., Dontchev A.L., “On the Bartle-Graves theorem”, Proc. Amer. Math. Soc., 131:8 (2003), 2553–2560  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Dontchev A.L., Lewis A.S., Rockafellar R.T., “The radius of metric regularity”, Trans. Amer. Math. Soc., 355:2 (2003), 493–517  crossref  mathscinet  zmath  isi
    9. Rubinov A.M., “Distance to the solution set of an inequality with an increasing function”, Equilibrium Problems and Variational Models, Nonconvex Optimization and its Applications, 68, 2003, 417–431  crossref  mathscinet  zmath  isi
    10. Dontchev A.L., “A local selection theorem for metrically regular mappings”, J. Convex Anal., 11:1 (2004), 81–94  mathscinet  zmath  isi
    11. Bosch P., Jourani A., Henrion R., “Sufficient conditions for error bounds and applications”, Appl. Math. Optim., 50:2 (2004), 161–181  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Zolezzi T., “On well-posedness and conditioning in optimization”, ZAMM Z. Angew. Math. Mech., 84:7 (2004), 435–443  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Dontchev A.L., Rockafellar R.T., “Regularity and conditioning of solution mappings in variational analysis”, Set-Valued Anal., 12:1-2 (2004), 79–109  crossref  mathscinet  zmath  isi  elib
    14. Huynh Van Ngai, Théra M., “Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization”, Set-Valued Anal., 12:1-2 (2004), 195–223  crossref  mathscinet  zmath  isi  elib
    15. Polyak B.T., “Convexity of the reachable set of nonlinear systems under $L_2$ bounded controls”, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 11:2-3 (2004), 255–267  mathscinet  zmath  isi  elib
    16. Kruger A., “Weak stationarity: eliminating the gap between necessary and sufficient conditions”, Optimization, 53:2 (2004), 147–164  crossref  mathscinet  zmath  isi  scopus  scopus
    17. “Boris Mordukhovich”, TOP, 13:2 (2005), 287–290  crossref
    18. Henrion R., Outrata J.V., “Calmness of constraint systems with applications”, Math. Program., 104:2-3, Ser. B (2005), 437–464  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Dmitruk A.V., “On a nonlocal metric regularity of nonlinear operators”, Control Cybernet., 34:3 (2005), 723–746  mathscinet  zmath  isi  elib
    20. Rolewicz S., “Paraconvex analysis”, Control Cybernet., 34:3 (2005), 951–965  mathscinet  zmath  isi
    21. Mordukhovich B.S., Wang Bingwu, “Restrictive metric regularity in variational analysis”, Nonlinear Anal., 63:5-7 (2005), 805–811  crossref  mathscinet  zmath  isi  scopus  scopus
    22. Dontchev A.L., Lewis A.S., “Perturbations and Metric regularity”, Set-Valued Anal., 13:4 (2005), 417–438  crossref  mathscinet  zmath  isi  scopus  scopus
    23. Cánovas M.J., Dontchev A.L., López M.A., Parra J., “Metric regularity of semi-infinite constraint systems”, Math. Program., 104:2-3, Ser. B (2005), 329–346  crossref  mathscinet  zmath  isi  scopus  scopus
    24. Uderzo A., “Fréchet quasidifferential calculus with applications to metric regularity of continuous maps”, Optimization, 54:4-5 (2005), 469–493  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    25. Rolewicz S., “On differentiability of strongly $\alpha(\cdot)$-paraconvex functions in non-separable Asplund spaces”, Studia Math., 167:3 (2005), 235–244  crossref  mathscinet  zmath  isi  scopus  scopus
    26. Ioffe A.D., “Optimality alternative: A non-variational approach tp necessary conditions”, Variational Analysis and Applications, Nonconvex Optimization and its Applications, 79, 2005, 531–552  crossref  mathscinet  zmath  isi
    27. Helmut Gfrerer, “Second-Order Optimality Conditions for Scalar and Vector Optimization Problems in Banach Spaces”, SIAM J Control Optim, 45:3 (2006), 972  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    28. Alexander Ya. Kruger, “About Regularity of Collections of Sets”, Set-Valued Anal, 14:2 (2006), 187  crossref  mathscinet  isi  scopus  scopus
    29. Aram V. Arutyunov, Alexey F. Izmailov, “Directional Stability Theorem and Directional Metric Regularity”, moor, 31:3 (2006), 526  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    30. Sjur Didrik Flam, “Upward Slopes and Inf-Convolutions”, moor, 31:1 (2006), 188  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    31. Joydeep Dutta, Christiane Tammer, “Lagrangian conditions for vector optimization in Banach spaces”, Mathematical Methods of OR, 64:3 (2006), 521  crossref  mathscinet  zmath  isi  scopus  scopus
    32. Rolewicz, S, “An extension of Mazur's theorem on Gateaux differentiability to the class of strongly alpha(center dot)-paraconvex functions”, Studia Mathematica, 172:3 (2006), 243  crossref  mathscinet  zmath  isi  scopus  scopus
    33. Avakov, ER, “Directional metric regularity of mappings and stability theorems”, Doklady Mathematics, 74:1 (2006), 473  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    34. Aze, D, “Variational methods in classical open mapping theorems”, Journal of Convex Analysis, 13:3–4 (2006), 477  mathscinet  zmath  isi
    35. Penot, JP, “The Fitzpatrick rate, the Stepanov rate, the Lipschitz rate and their relatives”, Journal of Convex Analysis, 13:3–4 (2006), 839  mathscinet  zmath  isi
    36. Klatte, D, “Stability of inclusions: characterizations via suitable Lipschitz functions and algorithms”, Optimization, 55:5–6 (2006), 627  crossref  mathscinet  zmath  isi  scopus  scopus
    37. Song, W, “Calmness and error bounds for convex constraint systems”, SIAM Journal on Optimization, 17:2 (2006), 353  crossref  mathscinet  zmath  isi  scopus  scopus
    38. Aze, D, “A unified theory for metric regularity of multifunctions”, Journal of Convex Analysis, 13:2 (2006), 225  mathscinet  zmath  isi
    39. Dontchev, AL, “Aubin criterion for metric regularity”, Journal of Convex Analysis, 13:2 (2006), 281  mathscinet  zmath  isi
    40. Aubin, JP, “A viability approach to the inverse set-valued map theorem”, Journal of Evolution Equations, 6:3 (2006), 419  crossref  mathscinet  zmath  isi  scopus  scopus
    41. Geoffroy, MH, “Approximation of fixed points of metrically regular mappings”, Numerical Functional Analysis and Optimization, 27:5–6 (2006), 565  crossref  mathscinet  zmath  isi  scopus  scopus
    42. Rolewicz, S, “On the Rockafellar theorem for Phi(gamma(.,.))-monotone multifunctions”, Studia Mathematica, 172:2 (2006), 197  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    43. Kruger A., “Stationarity and regularity concepts for set systems”, Systems, Control, Modeling and Optimization, International Federation for Information Processing, 202, 2006, 205–214  crossref  mathscinet  zmath  isi  scopus  scopus
    44. Xi Yin Zheng, Kung Fu Ng, “Metric Subregularity and Constraint Qualifications for Convex Generalized Equations in Banach Spaces”, SIAM J Optim, 18:2 (2007), 437  crossref  mathscinet  zmath  isi  scopus  scopus
    45. Aram V. Arutyunov, Evgeniy R. Avakov, Alexey F. Izmailov, “Directional Regularity and Metric Regularity”, SIAM J Optim, 18:3 (2007), 810  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    46. Ioffe, A, “On regularity estimates for mappings between embedded manifolds”, Control and Cybernetics, 36:3 (2007), 659  mathscinet  zmath  isi
    47. Sekiguchi, Y, “ON REGULARITY OF CONSTRAINT SYSTEMS WITH CONTINUOUS OPERATORS”, Journal of Nonlinear and Convex Analysis, 8:3 (2007), 357  mathscinet  zmath  isi
    48. Arutyunov, AV, “Covering mappings in metric spaces and fixed points”, Doklady Mathematics, 76:2 (2007), 665  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    49. Geoffroy, MH, “Regularity properties of a cubically convergent scheme for generalized equations”, Communications on Pure and Applied Analysis, 6:4 (2007), 983  crossref  mathscinet  zmath  isi
    50. Khanh, PQ, “Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives”, Journal of Optimization Theory and Applications, 133:3 (2007), 341  crossref  mathscinet  zmath  isi  scopus  scopus
    51. Artacho, FJA, “Uniformity and inexact version of a proximal method for metrically regular mappings”, Journal of Mathematical Analysis and Applications, 335:1 (2007), 168  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    52. Uderzo, A, “Convex difference criteria for the quantitative stability of parametric quasidifferentiable systems”, Set-Valued Analysis, 15:1 (2007), 81  crossref  mathscinet  zmath  isi  scopus  scopus
    53. Rolewicz, S, “Paraconvex analysis on C-E(1,u)-manifolds”, Optimization, 56:1–2 (2007), 49  crossref  mathscinet  zmath  isi  scopus  scopus
    54. Ng, KF, “Linear regularity and phi-regularity of nonconvex sets”, Journal of Mathematical Analysis and Applications, 328:1 (2007), 257  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    55. D. Azé, S. Benahmed, “On Implicit Multifunction Theorems”, Set-Valued Anal, 16:2-3 (2008), 129  crossref  mathscinet  zmath  isi  scopus  scopus
    56. Jean-Noël Corvellec, Viorica V. Motreanu, “Nonlinear error bounds for lower semicontinuous functions on metric spaces”, Math Program, 114:2 (2008), 291  crossref  mathscinet  zmath  isi  scopus  scopus
    57. P. Q. Khanh, N. D. Tuan, “Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions”, J Optim Theory Appl, 139:1 (2008), 47  crossref  mathscinet  zmath  isi  scopus  scopus
    58. Phan Quoc Khanh, Nguyen Dinh Tuan, “First and Second-Order Approximations as Derivatives of Mappings in Optimality Conditions for Nonsmooth Vector Optimization”, Appl Math Optim, 58:2 (2008), 147  crossref  mathscinet  zmath  isi  scopus  scopus
    59. Ioffe A.D., “An invitation to tame optimization”, SIAM J. Optim., 19:4 (2008), 1894–1917  crossref  mathscinet  isi  scopus
    60. Ursescu C., “Local uniform linear openness of multifunctions and calculus of Bouligand-Severi and Clarke tangent sets”, Taiwanese J. Math., 12:9 (2008), 2201–2231  crossref  mathscinet  zmath  isi  scopus
    61. Canovas, MJ, “On the Lipschitz Modulus of the Argmin Mapping in Linear Semi-Infinite Optimization”, Set-Valued Analysis, 16:5–6 (2008), 511  crossref  mathscinet  zmath  isi  scopus  scopus
    62. Canovas, MJ, “Stability of Indices in the KKT Conditions and Metric Regularity in Convex Semi-Infinite Optimization”, Journal of Optimization Theory and Applications, 139:3 (2008), 485  crossref  mathscinet  isi  scopus  scopus
    63. Canovas, MJ, “Lipschitz modulus of the optimal set mapping in convex optimization via minimal subproblems”, Pacific Journal of Optimization, 4:3 (2008), 411  mathscinet  zmath  isi
    64. Geoffroy, MH, “Iterative solving of variational inclusions under Wijsman perturbations”, Journal of Global Optimization, 42:1 (2008), 111  crossref  mathscinet  zmath  isi  scopus  scopus
    65. Mordukhovich, BS, “Failure of metric regularity for major classes of variational systems”, Nonlinear Analysis-Theory Methods & Applications, 69:3 (2008), 918  crossref  mathscinet  zmath  isi  scopus
    66. Artacho, FJA, “Characterization of metric regularity of sub differentials”, Journal of Convex Analysis, 15:2 (2008), 365  mathscinet  zmath  isi
    67. Van Ngai, H, “Error bounds in metric spaces and application to the perturbation stability of metric regularity”, SIAM Journal on Optimization, 19:1 (2008), 1  crossref  mathscinet  isi  elib  scopus  scopus
    68. Ioffe, AD, “On metric and calmness qualification conditions in subdifferential calculus”, Set-Valued Analysis, 16:2–3 (2008), 199  crossref  mathscinet  zmath  isi  scopus  scopus
    69. Ioffe, AD, “Critical values of set-valued maps with stratifiable graphs. Extensions of Sard and Smale-Sard theorems”, Proceedings of the American Mathematical Society, 136:9 (2008), 3111  crossref  mathscinet  zmath  isi  scopus  scopus
    70. Canovas, MJ, “Regularity modulus of arbitrarily perturbed linear inequality systems”, Journal of Mathematical Analysis and Applications, 343:1 (2008), 315  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    71. Luc, DT, “Equi-surjective systems of linear operators and applications”, Journal of Mathematical Analysis and Applications, 337:1 (2008), 266  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    72. Dmitruk, AV, “Metric regularity and systems of generalized equations”, Journal of Mathematical Analysis and Applications, 342:2 (2008), 864  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    73. Van Ngai, H, “Paraconvex functions and paraconvex sets”, Studia Mathematica, 184:1 (2008), 1  crossref  mathscinet  isi  scopus  scopus
    74. Canovas, MJ, “Lipschitz behavior of convex semi-infinite optimization problems: a variational approach”, Journal of Global Optimization, 41:1 (2008), 1  crossref  mathscinet  zmath  isi  scopus  scopus
    75. Demyanov, VF, “Exhausters and subdifferentials in non-smooth analysis”, Optimization, 57:1 (2008), 41  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    76. Hamel, AH, “Minimal elements for product orders”, Optimization, 57:2 (2008), 263  crossref  mathscinet  zmath  isi  scopus  scopus
    77. A. D. Ioffe, Y. Sekiguchi, “Regularity estimates for convex multifunctions”, Math Program, 117:1-2 (2009), 255  crossref  mathscinet  zmath  isi  scopus  scopus
    78. Diethard Klatte, Bernd Kummer, “Optimization methods and stability of inclusions in Banach spaces”, Math Program, 117:1-2 (2009), 305  crossref  mathscinet  zmath  isi  scopus  scopus
    79. Xi Yin Zheng, Kung Fu Ng, “Calmness for L-Subsmooth Multifunctions in Banach Spaces”, SIAM J Optim, 19:4 (2009), 1648  crossref  mathscinet  zmath  isi  scopus  scopus
    80. Xi Yin Zheng, Kung Fu Ng, “Strong KKT conditions and weak sharp solutions in convex-composite optimization”, Math Program, 2009  crossref  mathscinet  isi  scopus  scopus
    81. A. V. Arutyunov, “Stability of Coincidence Points and Properties of Covering Mappings”, Math. Notes, 86:2 (2009), 153–158  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    82. H. Th. Jongen, Jan.-J. Rückmann, V. Shikhman, “On Stability of the Feasible Set of a Mathematical Problem with Complementarity Problems”, SIAM J Optim, 20:3 (2009), 1171  crossref  mathscinet  zmath  isi  scopus  scopus
    83. Yoshiyuki Sekiguchi, “Exact estimates of regularity modulus for infinite programming”, Math Program, 2009  crossref  mathscinet  isi  scopus  scopus
    84. M. J. Canovas, M. A. Lopez, B. S. Mordukhovich, J. Parra, “Variational Analysis in Semi-Infinite and Infinite Programming, I: Stability of Linear Inequality Systems of Feasible Solutions”, SIAM J Optim, 20:3 (2009), 1504  crossref  mathscinet  zmath  isi
    85. Zheng Xi Yin, Ng Kung Fu, “Metric regularity of composite multifunctions in Banach spaces”, Taiwanese J. Math., 13:6A (2009), 1723–1735  crossref  mathscinet  zmath  isi  scopus
    86. Kruger A.Y., “About stationarity and regularity in variational analysis”, Taiwanese J. Math., 13:6A (2009), 1737–1785  crossref  mathscinet  zmath  isi  scopus
    87. Leventhal, D, “Metric subregularity and the proximal point method”, Journal of Mathematical Analysis and Applications, 360:2 (2009), 681  crossref  mathscinet  zmath  isi  scopus
    88. Cánovas M.J., Hantoute A., López M.A., Parra J., “Lipschitz modulus in convex semi-infinite optimization via d.c. functions”, ESAIM Control Optim. Calc. Var., 15:4 (2009), 763–781  crossref  mathscinet  zmath  isi  scopus
    89. Dmitruk, AV, “Extensions of metric regularity”, Optimization, 58:5 (2009), 561  crossref  mathscinet  zmath  isi  elib  scopus
    90. Arutyunov A.V., “Stability of coincidence points and set-valued covering maps in metric spaces”, Dokl. Math., 80:1 (2009), 555–557  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    91. Geoffroy, MH, “Stability of Mann's iterates under metric regularity”, Applied Mathematics and Computation, 215:2 (2009), 686  crossref  mathscinet  zmath  isi  scopus
    92. Movahedian, N, “Nondifferentiable Multiplier Rules for Optimization Problems with Equilibrium Constraints”, Journal of Convex Analysis, 16:1 (2009), 187  mathscinet  zmath  isi
    93. Kummer, B, “Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland's principle”, Journal of Mathematical Analysis and Applications, 358:2 (2009), 327  crossref  mathscinet  zmath  isi  elib  scopus
    94. Gaydu, M, “Tikhonov regularization of metrically regular inclusions”, Positivity, 13:2 (2009), 385  crossref  mathscinet  zmath  isi  scopus
    95. Durea, M, “Fuzzy necessary optimality conditions for vector optimization problems”, Optimization, 58:4 (2009), 449  crossref  mathscinet  zmath  isi  scopus
    96. Arutyunov A., Avakov E., Gel'man B., Dmitruk A., Obukhovskii V., “Locally covering maps in metric spaces and coincidence points”, J. Fixed Point Theory Appl., 5:1 (2009), 105–127  crossref  mathscinet  zmath  isi  elib  scopus
    97. Aze, D, “On some variational properties of metric spaces”, Journal of Fixed Point Theory and Applications, 5:1 (2009), 185  crossref  mathscinet  zmath  isi  scopus
    98. Geoffroy, MH, “An inertial proximal scheme for nonmonotone mappings”, Journal of Mathematical Analysis and Applications, 350:1 (2009), 147  crossref  mathscinet  zmath  isi  scopus  scopus
    99. Geremew, W, “Coderivative calculus and metric regularity for constraint and variational systems”, Nonlinear Analysis-Theory Methods & Applications, 70:1 (2009), 529  crossref  mathscinet  zmath  isi  scopus  scopus
    100. Mordukhovich B.S., Nguyen Mau Nam, Bingwu Wang, “Metric regularity of mappings and generalized normals to set images”, Set-Valued Anal., 17:4 (2009), 359–387  crossref  mathscinet  zmath  isi  scopus  scopus
    101. Uderzo A., “On some regularity properties in variational analysis”, Set-Valued Anal., 17:4 (2009), 409–430  crossref  mathscinet  zmath  isi  scopus  scopus
    102. Mordukhovich B.S., “New Applications of Variational Analysis to Optimization and Control”, System Modeling and Optimization, Ifip Advances in Information and Communication Technology, 312, 2009, 100–128  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    103. Penot J.-P., “Ekeland Duality as a Paradigm”, Advances in Applied Mathematics and Global Optimization, Advances in Mechanics and Mathematics, 17, 2009, 349–376  crossref  mathscinet  zmath  isi
    104. Canovas, MJ, “Linear regularity, equirregularity, and intersection mappings for convex semi-infinite inequality systems”, Mathematical Programming, 123:1 (2010), 33  crossref  mathscinet  zmath  isi  scopus  scopus
    105. Ioffe, AD, “Towards variational analysis in metric spaces: metric regularity and fixed points”, Mathematical Programming, 123:1 (2010), 241  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    106. Artacho F.J.A., Mordukhovich B.S., “Metric regularity and Lipschitzian stability of parametric variational systems”, Nonlinear Anal., 72:3-4 (2010), 1149–1170  crossref  mathscinet  zmath  isi  scopus  scopus
    107. Fabian M.J., Henrion R., Kruger A.Y., Outrata J.V., “Error bounds: necessary and sufficient conditions”, Set-Valued Anal., 18:2 (2010), 121–149  crossref  mathscinet  zmath  isi  scopus  scopus
    108. Xi Yin Zheng, Kung Fu Ng, “Metric subregularity and calmness for nonconvex generalized equations in Banach spaces”, SIAM J. Optim., 20:5 (2010), 2119–2136  crossref  mathscinet  zmath  isi  scopus  scopus
    109. Henrion R., Mordukhovich B.S., Nguyen Mau Nam, “Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities”, SIAM J. Optim., 20:5 (2010), 2199–2227  crossref  mathscinet  zmath  isi  scopus  scopus
    110. Xi Yin Zheng, Kung Fu Ng, “Metric subregularity for nonclosed convex multifunctions in normed spaces”, ESAIM COCV, 16:3 (2010), 601  crossref  mathscinet  zmath  isi  scopus  scopus
    111. Hélène Frankowska, Marc Quincampoix, “Hölder metric regularity of set-valued maps”, Math Program, 2010  crossref  mathscinet  isi  scopus  scopus
    112. Oana Silvia Serea, Lionel Thibault, “Primal-Lower-Nice Property of Value Functions in Optimization and Control Problems”, Set-Valued Anal, 2010  crossref  mathscinet  isi  scopus  scopus
    113. Michaël Gaydu, Michel H. Geoffroy, Célia Jean-Alexis, “Metric subregularity of order q and the solving of inclusions”, centr.eur.j.math, 9:1 (2010), 147  crossref  mathscinet  isi  scopus  scopus
    114. Ioffe A.D., “On regularity concepts in variational analysis”, Journal of Fixed Point Theory and Applications, 8:2 (2010), 339–363  crossref  mathscinet  zmath  isi  scopus  scopus
    115. Gong X.-H., “Scalarization and optimality conditions for vector equilibrium problems”, Nonlinear Analysis-Theory Methods & Applications, 73:11 (2010), 3598–3612  crossref  mathscinet  zmath  isi  scopus  scopus
    116. Uderzo A., “Exact penalty functions and calmness for mathematical programming under nonlinear perturbations”, Nonlinear Analysis-Theory Methods & Applications, 73:6 (2010), 1596–1609  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    117. Nam N.M., “Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities”, Nonlinear Analysis-Theory Methods & Applications, 73:7 (2010), 2271–2282  crossref  mathscinet  zmath  isi  scopus  scopus
    118. Bolte J., Daniilidis A., Ley O., Mazet L., “Characterizations of Lojasiewicz Inequalities: Subgradient Flows, Talweg, Convexity”, Transactions of the American Mathematical Society, 362:6 (2010), 3319–3363  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    119. Ioffe A.D., “The Principle of Lagrange and Critical Values of Optimization Problems”, Pacific Journal of Optimization, 6:2 (2010), 341–352  mathscinet  zmath  isi
    120. Attouch H., Bolte J., Redont P., Soubeyran A., “Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality”, Mathematics of Operations Research, 35:2 (2010), 438–457  crossref  mathscinet  zmath  isi  scopus  scopus
    121. Correa R., Gajardo P., Thibault L., “Various Lipschitz-Like Properties for Functions and Sets i: Directional Derivative and Tangential Characterizations”, SIAM Journal on Optimization, 20:4 (2010), 1766–1785  crossref  mathscinet  zmath  isi  scopus  scopus
    122. Zheng X., Wei Zh., Yao J.-Ch., “Uniform subsmoothness and linear regularity for a collection of infinitely many closed sets”, Nonlinear Analysis-Theory Methods & Applications, 73:2 (2010), 413–430  crossref  mathscinet  zmath  isi  scopus  scopus
    123. Uderzo A., “On a perturbation approach to open mapping theorems”, Optimization Methods & Software, 25:1 (2010), 143–167  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    124. Canovas M.J., Hantoute A., Lopez M.A., Parra J., “A note on the compactness of the index set in convex optimization. Application to metric regularity”, Optimization, 59:4 (2010), 477–483  crossref  mathscinet  zmath  isi  scopus  scopus
    125. Demyanov V.F., “Nonsmooth Optimization”, Nonlinear Optimization, Lecture Notes in Mathematics, 1989, 2010, 55–163  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    126. Baier R., Farkhi E., “The Directed Subdifferential of DC Functions”, Nonlinear Analysis and Optimization II: Optimization, Contemporary Mathematics, 514, 2010, 27–43  crossref  mathscinet  zmath  isi
    127. Giannessi F., Moldovan A., Pellegrini L., “Metric Regular Maps and Regularity for Constrained Extremum Problems”, Nonlinear Analysis and Optimization II: Optimization, Contemporary Mathematics, 514, 2010, 143–154  crossref  mathscinet  zmath  isi
    128. Penot J.-P., “Error Bounds, Calmness and their Applications in Nonsmooth Analysis”, Nonlinear Analysis and Optimization II: Optimization, Contemporary Mathematics, 514, 2010, 225–247  crossref  mathscinet  zmath  isi
    129. Xi Yin Zheng, Wei Ouyang, “Metric subregularity for composite-convex generalized equations in Banach spaces”, Nonlinear Analysis: Theory, Methods & Applications, 74:10 (2011), 3311  crossref  mathscinet  zmath  isi  scopus  scopus
    130. Truong Xuan Duc Ha, “Optimality conditions for various efficient solutions involving coderivatives: From set-valued optimization problems to set-valued equilibrium problems”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    131. A. Uderzo, “On mappings covering at a nonlinear rate and their perturbation stability”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    132. Ewa M. Bednarczuk, Alexander Y. Kruger, “Error bounds for vector-valued functions: Necessary and sufficient conditions”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    133. T. Hoheisel, C. Kanzow, B.S. Mordukhovich, H. Phan, “Generalized Newton’s method based on graphical derivatives”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  zmath  isi  scopus  scopus
    134. Marco A. López, Andrea B. Ridolfi, Virginia N. Vera de Serio, “On coderivatives and Lipschitzian properties of the dual pair in optimization”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    135. Xi Yin Zheng, Kung-Fu Ng, “Metric subregularity for proximal generalized equations in Hilbert spaces”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    136. Robert Baier, Elza Farkhi, Vera Roshchina, “The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    137. Alexander Kruger, “Comments on: Stability in linear optimization and related topics. A personal tour”, TOP, 2011  crossref  mathscinet  isi  scopus  scopus
    138. M. J. Cánovas, M. A. López, B. S. Mordukhovich, J. Parra, “Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems”, TOP, 2011  crossref  mathscinet  isi  scopus  scopus
    139. Amos Uderzo, “A Metric Version of Milyutin Theorem”, Set-Valued Anal, 2011  crossref  mathscinet  isi  scopus  scopus
    140. Nooshin Movahedian, “Calmness and inverse image characterizations for Asplund spaces”, Optim Lett, 2011  crossref  mathscinet  isi  scopus  scopus
    141. Helmut Gfrerer, “First Order and Second Order Characterizations of Metric Subregularity and Calmness of Constraint Set Mappings”, SIAM J. Optim, 21:4 (2011), 1439  crossref  mathscinet  zmath  isi  scopus  scopus
    142. Ioffe A.D., “Regularity on a Fixed Set”, SIAM J Optim, 21:4 (2011), 1345–1370  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    143. Li Sh., Penot J.-P., Xue X., “Codifferential Calculus”, Set Valued Var Anal, 19:4 (2011), 505–536  crossref  mathscinet  zmath  isi  scopus  scopus
    144. Pang C.H.J., “Generalized Differentiation with Positively Homogeneous Maps: Applications in Set-Valued Analysis and Metric Regularity”, Math Oper Res, 36:3 (2011), 377–397  crossref  mathscinet  zmath  isi  scopus  scopus
    145. Aragon Artacho F.J., Dontchev A.L., Gaydu M., Geoffroy M.H., Veliov V.M., “Metric Regularity of Newton's Iteration”, SIAM J Control Optim, 49:2 (2011), 339–362  crossref  mathscinet  zmath  isi  scopus  scopus
    146. Bernard F., Thibault L., Zlateva N., “Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties”, Trans Amer Math Soc, 363:4 (2011), 2211–2247  crossref  mathscinet  zmath  isi  scopus  scopus
    147. Ioffe A.D., “Separable reduction revisited”, Optimization, 60:1–2 (2011), 211–221  crossref  mathscinet  zmath  isi  scopus  scopus
    148. Li M.H., Li S.J., “Robinson metric regularity of parametric variational systems”, Nonlinear Analysis-Theory Methods & Applications, 74:6 (2011), 2262–2271  crossref  mathscinet  zmath  isi  scopus  scopus
    149. Dontchev A.L., Frankowska H., “Lyusternik-Graves Theorem and Fixed Points”, Proc Amer Math Soc, 139:2 (2011), 521–534  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    150. A.V.ahidian Kamyad, M.H.a.N.oori Skandari, H.R.eza Erfanian, “A New Definition for Generalized First Derivative of Nonsmooth Functions”, AM, 02:10 (2011), 1252  crossref  mathscinet
    151. Nguyen Mau Nam, Bingwu Wang, “Metric regularity, tangential distances and generalized differentiation in Banach spaces”, Nonlinear Analysis: Theory, Methods & Applications, 75:3 (2012), 1496  crossref  mathscinet  zmath  isi  scopus  scopus
    152. Durea M., Strugariu R., “Openness stability and implicit multifunction theorems: Applications to variational systems”, Nonlinear Analysis-Theory Methods & Applications, 75:3 (2012), 1246–1259  crossref  mathscinet  zmath  isi  scopus  scopus
    153. Bettiol P., Frankowska H., “Lipschitz Regularity of Solution Map of Control Systems With Multiple State Constraints”, Discrete and Continuous Dynamical Systems, 32:1 (2012), 1–26  mathscinet  zmath  isi
    154. Alexander Y. Kruger, Marco A. López, “Stationarity and Regularity of Infinite Collections of Sets”, J Optim Theory Appl, 2012  crossref  mathscinet  isi  scopus  scopus
    155. Marius Durea, Radu Strugariu, “Chain Rules for Linear Openness in General Banach Spaces”, SIAM J. Optim, 22:3 (2012), 899  crossref  mathscinet  zmath  isi  scopus  scopus
    156. Aris Daniilidis, Miguel A. Goberna, Marco A. López, Roberto Lucchetti, “Lower Semicontinuity of the Feasible Set Mapping of Linear Systems Relative to Their Domains”, Set-Valued Var. Anal, 2012  crossref  mathscinet  isi  scopus  scopus
    157. Helmut Gfrerer, “On Directional Metric Regularity, Subregularity and Optimality Conditions for Nonsmooth Mathematical Programs”, Set-Valued Var. Anal, 2012  crossref  mathscinet  isi  scopus  scopus
    158. Marius Durea, Radu Strugariu, “Chain rules for linear openness in metric spaces and applications”, Math. Program, 2012  crossref  mathscinet  isi  scopus  scopus
    159. T. T. A. Nghia, “A note on implicit multifunction theorems”, Optim Lett, 2012  crossref  mathscinet  isi  scopus  scopus
    160. René Henrion, “Gradient estimates for Gaussian distribution functions: application to probabilistically constrained optimization problems”, NACO, 2:4 (2012), 655  crossref  mathscinet  zmath  scopus  scopus
    161. Guoyin Li, Boris S. Mordukhovich, “Hölder Metric Subregularity with Applications to Proximal Point Method”, SIAM J. Optim, 22:4 (2012), 1655  crossref  mathscinet  zmath  isi  scopus  scopus
    162. S. Hosseini, M. R. Pouryayevali, “Nonsmooth Optimization Techniques on Riemannian Manifolds”, J Optim Theory Appl, 2012  crossref  mathscinet  isi  scopus  scopus
    163. Gaydu M., “Stability Properties of the Tikhonov Regularization for Nonmonotone Inclusions”, J. Glob. Optim., 52:4 (2012), 843–853  crossref  mathscinet  zmath  isi  scopus  scopus
    164. Tamasyan G.Sh., “O metodakh naiskoreishego i gipodifferentsialnogo spuska v odnoi zadache variatsionnogo ischisleniya”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 13:1 (2012), 197–217  mathnet  elib
    165. Canovas M.J., Gomez-Senent F.J., Parra J., “Regularity Modulus of Intersection Mappings. Application to the Stability of Equations via Splitting Into Inequalities”, J. Convex Anal., 19:4, SI (2012), 913–926  mathscinet  zmath  isi
    166. Dontchev A.L. Frankowska H., “Lyusternik-Graves Theorem and Fixed Points II”, J. Convex Anal., 19:4, SI (2012), 955–973  mathscinet  zmath  isi  elib
    167. Ioffe A.D., “On Stability of Solutions to Systems of Convex Inequalities”, J. Convex Anal., 19:4, SI (2012), 1017–1032  mathscinet  zmath  isi
    168. Klatte D., Kruger A., Kummer B., “From Convergence Principles to Stability and Optimality Conditions”, J. Convex Anal., 19:4, SI (2012), 1043–1072  mathscinet  zmath  isi  elib
    169. C. H. Jeffrey Pang, “Characterizing Generalized Derivatives of Set-Valued Maps: Extending the Tangential and Normal Approaches”, SIAM J. Control Optim, 51:1 (2013), 145  crossref  mathscinet  zmath  isi  scopus  scopus
    170. D. Drusvyatskiy, A. S. Lewis, “Tilt Stability, Uniform Quadratic Growth, and Strong Metric Regularity of the Subdifferential”, SIAM J. Optim, 23:1 (2013), 256  crossref  mathscinet  zmath  isi  scopus  scopus
    171. Marius Durea, Huu Tron Nguyen, Radu Strugariu, “Metric regularity of epigraphical multivalued mappings and applications to vector optimization”, Math. Program, 2013  crossref  mathscinet  isi  scopus  scopus
    172. Alexander D. Ioffe, “Nonlinear regularity models”, Math. Program, 2013  crossref  mathscinet  isi  scopus  scopus
    173. Helmut Gfrerer, “On Directional Metric Subregularity and Second-Order Optimality Conditions for a Class of Nonsmooth Mathematical Programs”, SIAM J. Optim, 23:1 (2013), 632  crossref  mathscinet  zmath  isi  scopus  scopus
    174. YONGCHAO LIU, “STABILITY ANALYSIS OF PARAMETRIC GENERALIZED EQUATIONS AND APPLICATIONS”, Asia Pac. J. Oper. Res, 2013, 1350017  crossref  mathscinet  zmath  isi  scopus  scopus
    175. v.N.gai Huynh, H.T.ron Nguyen, Michel Théra, “Implicit multifunction theorems in complete metric spaces”, Math. Program, 2013  crossref  mathscinet  isi  scopus  scopus
    176. Hà Huy Vui, “Global Hölderian Error Bound for Nondegenerate Polynomials”, SIAM J. Optim, 23:2 (2013), 917  crossref  mathscinet  zmath  isi  scopus  scopus
    177. Mercedes Larriqueta, V.N.. Vera de Serio, “On Metric Regularity and the Boundary of the Feasible Set in Linear Optimization”, Set-Valued Var. Anal, 2013  crossref  mathscinet  isi  scopus  scopus
    178. Zhou Wei, Jen-Chih Yao, Zheng, “Strong Abadie CQ, ACQ, calmness and linear regularity”, Math. Program, 2013  crossref  mathscinet  isi  scopus  scopus
    179. Bingwu Wang, Mingming Zhu, Yali Zhao, Weiyi Qian, “Structure and stability of restrictively metrically regular mappings”, Nonlinear Analysis: Theory, Methods & Applications, 90 (2013), 27  crossref  mathscinet  zmath  isi  scopus  scopus
    180. X. J. Long, N. J. Huang, “Optimality conditions for minimizing the difference of nonconvex vector-valued mappings”, Optim Lett, 2013  crossref  mathscinet  isi  scopus  scopus
    181. Ngai, N.H.uu Tron, Michel Théra, “Metric Regularity of the Sum of Multifunctions and Applications”, J Optim Theory Appl, 2013  crossref  mathscinet  isi  scopus  scopus
    182. C. Gutiérrez, B. Jiménez, V. Novo, “Optimality Conditions for Quasi-Solutions of Vector Optimization Problems”, J Optim Theory Appl, 2013  crossref  isi  scopus  scopus
    183. Marius Durea, V.N.gai Huynh, H.T.ron Nguyen, Radu Strugariu, “Metric regularity of composition set-valued mappings: Metric setting and coderivative conditions”, Journal of Mathematical Analysis and Applications, 2013  crossref  mathscinet  isi  scopus  scopus
    184. A. Uderzo, “On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization”, J Optim Theory Appl, 2013  crossref  mathscinet  isi  scopus  scopus
    185. Helmut Gfrerer, “On Metric Pseudo-(sub)Regularity of Multifunctions and Optimality Conditions for Degenerated Mathematical Programs”, Set-Valued Var. Anal, 2013  crossref  mathscinet  isi  scopus  scopus
    186. V. F. Demyanov, M. V. Dolgopolik, “Kodifferentsiruemye funktsii v banakhovykh prostranstvakh: metody i  prilozheniya k  zadacham variatsionnogo ischisleniya”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2013, no. 3, 48–66  mathnet
    187. Robert Hesse, D. Russell Luke, “Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems”, SIAM J. Optim, 23:4 (2013), 2397  crossref  mathscinet  zmath  isi  scopus  scopus
    188. Cibulka R., Fabian M., “A Note on Robinson-Ursescu and Lyusternik-Graves Theorem”, Math. Program., 139:1-2, SI (2013), 89–101  crossref  mathscinet  zmath  isi  scopus  scopus
    189. Zheng, K.F.u Ng, “Metric Subregularity of Piecewise Linear Multifunctions and Applications to Piecewise Linear Multiobjective Optimization”, SIAM J. Optim, 24:1 (2014), 154  crossref  mathscinet  zmath  isi  scopus  scopus
    190. Zheng, He, “Characterization of metric regularity for -subsmooth multifunctions”, Nonlinear Analysis: Theory, Methods & Applications, 100 (2014), 111  crossref  mathscinet  zmath  isi  scopus  scopus
    191. C. H. Jeffrey Pang, “Set intersection problems: supporting hyperplanes and quadratic programming”, Math. Program, 2014  crossref  mathscinet  isi  scopus  scopus
    192. M. J. Cánovas, M. A. López, J. Parra, F. J. Toledo, “Calmness of the Feasible Set Mapping for Linear Inequality Systems”, Set-Valued Var. Anal, 2014  crossref  mathscinet  isi  scopus  scopus
    193. A.Y.. Kruger, N.H.. Thao, “About -regularity properties of collections of sets”, Journal of Mathematical Analysis and Applications, 2014  crossref  mathscinet  isi  scopus  scopus
    194. A. Jourani, T. Zakaryan, “The validity of the “” formula and a characterization of Asplund spaces”, Journal of Mathematical Analysis and Applications, 2014  crossref  mathscinet  isi  scopus  scopus
    195. A.Y.. Kruger, N.H.. Thao, “Quantitative Characterizations of Regularity Properties of Collections of Sets”, J Optim Theory Appl, 2014  crossref  mathscinet  isi  scopus  scopus
    196. Jiangxing Zhu, Qinghai He, Jinchuan Lin, “Error Bound for Conic Inequality in Hilbert Spaces”, Abstract and Applied Analysis, 2014 (2014), 1  crossref  mathscinet  isi  scopus  scopus
    197. B.S.. Mordukhovich, T. T. A. Nghia, “Nonsmooth Cone-Constrained Optimization with Applications to Semi-Infinite Programming”, Mathematics of OR, 39:2 (2014), 301  crossref  mathscinet  zmath  isi  scopus  scopus
    198. Shengkun Zhu, Shengjie Li, “Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints”, Abstract and Applied Analysis, 2014 (2014), 1  crossref  mathscinet  isi  scopus  scopus
    199. Helmut Gfrerer, “Optimality Conditions for Disjunctive Programs Based on Generalized Differentiation with Application to Mathematical Programs with Equilibrium Constraints”, SIAM J. Optim, 24:2 (2014), 898  crossref  mathscinet  zmath  isi  scopus  scopus
    200. J. J. Wang, W. Song, “Characterization of the Strong Metric Subregularity of the Mordukhovich Subdifferential on Asplund Spaces”, Abstract and Applied Analysis, 2014 (2014), 1  crossref  isi  scopus  scopus
    201. A. Uderzo, “Some Dual Conditions for Global Weak Sharp Minimality of Nonconvex Functions”, Numerical Functional Analysis and Optimization, 35:7-9 (2014), 1258  crossref  mathscinet  zmath  isi  scopus  scopus
    202. A.Y.. Kruger, “Error bounds and metric subregularity”, Optimization, 2014, 1  crossref  mathscinet  isi  scopus  scopus
    203. Zheng, K.F.u Ng, “Error Bound for Conic Inequality”, Vietnam J. Math, 2014  crossref  mathscinet  scopus  scopus
    204. M. V. Dolgopolik, G. Sh. Tamasyan, “Ob ekvivalentnosti metodov naiskoreishego i gipodifferentsialnogo spuskov v nekotorykh zadachakh uslovnoi optimizatsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 532–542  mathnet
    205. Hesse R., Luke D.R., Neumann P., “Alternating Projections and Douglas-Rachford For Sparse Affine Feasibility”, IEEE Trans. Signal Process., 62:18 (2014), 4868–4881  crossref  mathscinet  isi  scopus  scopus
    206. Chao M.-T., Cheng C.-Z., “Nonlinear Metric Regularity and Subregularity”, Pac. J. Optim., 10:2 (2014), 275–284  mathscinet  zmath  isi
    207. Ioffe A.D., “Metric Regularity, Fixed Points and Some Associated Problems of Variational Analysis”, J. Fixed Point Theory Appl., 15:1 (2014), 67–99  crossref  mathscinet  zmath  isi  scopus  scopus
    208. Drusvyatsldy D., Mordukhovich B.S., Nhgia T.T.A., “Second-Order Growth, Tilt Stability, and Metric Regularity of the Subdifferential”, J. Convex Anal., 21:4 (2014), 1165–1192  mathscinet  isi
    209. Uderzo A., “Calmness of Nonsmooth Constraint Systems: Dual Conditions Via Scalarized Exhausters”, J. Convex Anal., 21:2 (2014), 507–534  mathscinet  zmath  isi
    210. A. D. Ioffe, “On necessary conditions for a minimum”, J. Math. Sci., 217:6 (2016), 751–772  mathnet  crossref  mathscinet
    211. Liqun Ban, Wen Song, “Linearly perturbed generalized polyhedral normal cone mappings and applications”, Optimization, 2015, 1  crossref  isi  scopus  scopus
    212. Ngai, Ph.N.hat Tinh, “Metric Subregularity of Multifunctions: First and Second Order Infinitesimal Characterizations”, Mathematics of OR, 2015, 1502021116  crossref  mathscinet  isi  scopus  scopus
    213. Zheng, K.F.u Ng, “Hölder Stable Minimizers, Tilt Stability, and Hölder metric Regularity of Subdifferentials”, SIAM J. Optim, 25:1 (2015), 416  crossref  mathscinet  zmath  isi  scopus  scopus
    214. D. Azé, J. -N. Corvellec, “Nonlinear local error bounds via a change of metric”, J. Fixed Point Theory Appl, 2015  crossref  mathscinet  isi  scopus  scopus
    215. Zheng, Kung-Fu Ng, “Hölder weak sharp minimizers and Hölder tilt-stability”, Nonlinear Analysis: Theory, Methods & Applications, 120 (2015), 186  crossref  mathscinet  zmath  isi  scopus  scopus
    216. Bianchi M., Kassay G., Pini R., “Stability Results of Variational Systems Under Openness With Respect To Fixed Sets”, J. Optim. Theory Appl., 164:1 (2015), 92–108  crossref  mathscinet  zmath  isi  scopus  scopus
    217. A. V. Arutyunov, E. R. Avakov, S. E. Zhukovskiy, “Stability Theorems for Estimating the Distance to a Set of Coincidence Points”, SIAM J. Optim, 25:2 (2015), 807  crossref  mathscinet  zmath  isi  scopus  scopus
    218. A.Y.. Kruger, “Error Bounds and Hölder Metric Subregularity”, Set-Valued Var. Anal, 2015  crossref  mathscinet  isi  scopus  scopus
    219. Radek Cibulka, Marián Fabian, A.D.. Ioffe, “On primal regularity estimates for single-valued mappings”, J. Fixed Point Theory Appl, 2015  crossref  mathscinet  isi  scopus  scopus
    220. E. R. Avakov, “Stability theorem and extremum conditions for abnormal problems”, Proc. Steklov Inst. Math., 291 (2015), 4–23  mathnet  crossref  crossref  isi  elib
    221. Drusvyatskiy D., Ioffe A.D., Lewis A.S., “Transversality and Alternating Projections For Nonconvex Sets”, 15, no. 6, 2015, 1637–1651  crossref  mathscinet  zmath  isi  scopus  scopus
    222. Huynh Van Ngai Thera M., “Directional Metric Regularity of Multifunctions”, 40, no. 4, 2015, 969–991  crossref  mathscinet  zmath  isi  scopus  scopus
    223. Khanh Ph.Q., Kruger A.Y., Thao N.H., “An Induction Theorem and Nonlinear Regularity Models”, 25, no. 4, 2015, 2561–2588  crossref  mathscinet  zmath  isi  scopus  scopus
    224. Li R., Yao J.-Ch., Zheng X.Y., “Approximate Kkt Points For Smooth Vector Optimization Problems in Infinite Dimensional Spaces”, 16, no. 7, SI, 2015, 1385–1396  mathscinet  zmath  isi
    225. Mlesnite O., Petrusel A., “Metric Regularity and Ulam-Hyers Stability Results For Coincidence Problems With Multivalued Operators”, 16, no. 7, SI, 2015, 1397–1413  mathscinet  zmath  isi
    226. Drusvyatskiy D., Ioffe A.D., Lewis A.S., “Curves of Descent”, 53, no. 1, 2015, 114–138  crossref  mathscinet  zmath  isi  scopus  scopus
    227. Mlesnite O., “Covering Mappings and Ulam-Hyers Stability Results For Coincidence Problems”, 31, no. 1, 2015, 97–104  mathscinet  zmath  isi
    228. I. V. Orlov, S. I. Smirnova, “Invertibility of multivalued sublinear operators”, Eurasian Math. J., 6:4 (2015), 44–58  mathnet
    229. Kruger A.Y., Plubtieng S., Seangwattana T., “Borwein-Preiss Variational Principle Revisited”, 435, no. 2, 2016, 1183–1193  crossref  mathscinet  zmath  isi  scopus  scopus
    230. Dung Phi Hoang, “Lojasiewicz-Type Inequalities and Global Error Bounds For Nonsmooth Definable Functions in O-Minimal Structures”, 93, no. 1, 2016, 99–112  crossref  mathscinet  zmath  isi  scopus  scopus
    231. I. V. Orlov, “Inverse and Implicit Function Theorems in the Class of Subsmooth Maps”, Math. Notes, 99:4 (2016), 619–622  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    232. S. E. Zhukovskiy, Z. T. Zhukovskaya, “Algorithm for computing the covering constant of a linear operator on a cone”, Comput. Math. Math. Phys., 56:8 (2016), 1373–1381  mathnet  crossref  crossref  isi  elib
    233. Thao N.H., “Regularity Properties in Variational Analysis and Applications in Optimisation”, Bull. Aust. Math. Soc., 93:3 (2016), 523–524  crossref  mathscinet  zmath  isi  scopus
    234. Durea M. Strugariu R., “Metric Subregularity of Composition Set-Valued Mappings with Applications to Fixed Point Theory”, Set-Valued Var. Anal., 24:2 (2016), 231–251  crossref  mathscinet  zmath  isi  scopus
    235. Cibulka R., Fabian M., “On primal regularity estimates for set-valued mappings”, J. Math. Anal. Appl., 438:1 (2016), 444–464  crossref  mathscinet  zmath  isi  scopus
    236. Wang J.J., Song W., “Characterization of quadratic growth of extended-real-valued functions”, J. Inequal. Appl., 2016, 29  crossref  mathscinet  isi  scopus
    237. Dolgopolik M.V., “A unifying theory of exactness of linear penalty functions”, Optimization, 65:6 (2016), 1167–1202  crossref  mathscinet  zmath  isi  elib  scopus
    238. Drusvyatskiy D., Ioffe A.D., Lewis A.S., “Generic Minimizing Behavior in Semialgebraic Optimization”, SIAM J. Optim., 26:1 (2016), 513–534  crossref  mathscinet  zmath  isi  scopus
    239. Zheng X.Y., Zhu J., “Generalized Metric Subregularity and Regularity with Respect to an Admissible Function”, SIAM J. Optim., 26:1 (2016), 535–563  crossref  mathscinet  zmath  isi  scopus
    240. Zheng X.Y., “Metric Subregularity for a Multifunction”, J. Math. Study, 49:4 (2016), 379–392  crossref  mathscinet  zmath  isi
    241. Soleimani B., Tammer C., “Optimality Conditions For Approximate Solutions of Vector Optimization Problems With Variable Ordering Structures”, Bull. Iran Math. Soc., 42:7, SI (2016), 5–23  mathscinet  zmath  isi
    242. Huynh Van Ngai, Nguyen Huu Tron, Thera M., “Directional Hölder Metric Regularity”, J. Optim. Theory Appl., 171:3 (2016), 785–819  crossref  mathscinet  zmath  isi  scopus
    243. Kruger A.Y., “Nonlinear Metric Subregularity”, J. Optim. Theory Appl., 171:3 (2016), 820–855  crossref  mathscinet  zmath  isi  scopus
    244. Ioffe A.D., “Metric Regularity-a Survey Part II. Applications”, J. Aust. Math. Soc., 101:3 (2016), 376–417  crossref  mathscinet  zmath  isi  elib  scopus
    245. Baier R., Farkhi E., Roshchina V., “From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules”, J. Optim. Theory Appl., 171:2 (2016), 384–401  crossref  mathscinet  zmath  isi  scopus
    246. Ioffe A.D., “Metric Regularity-a Survey Part 1. Theory”, J. Aust. Math. Soc., 101:2 (2016), 188–243  crossref  mathscinet  zmath  isi  elib  scopus
    247. Fabian M., Ioffe A., “Separable Reductions and Rich Families in the Theory of Frechet Subdifferentials”, J. Convex Anal., 23:3 (2016), 631–648  mathscinet  zmath  isi
    248. Kruger A.Y., Thao N.H., “Regularity of Collections of Sets and Convergence of Inexact Alternating Projections”, J. Convex Anal., 23:3 (2016), 823–847  mathscinet  zmath  isi
    249. Zhang B., Ng K.-F., Zheng X.Y., He Q., “Hölder metric subregularity for multifunctions in type Banach spaces”, Optimization, 65:11 (2016), 1963–1982  crossref  mathscinet  zmath  isi  scopus
    250. M. I. Gusev, I. V. Zykov, “On extremal properties of the boundary points of reachable sets for control systems with integral constraints”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 114–125  mathnet  crossref  crossref  isi  elib
    251. Alleche B. Radulescu V.D., “Inverse of the Sum of Set-Valued Mappings and Applications”, Numer. Funct. Anal. Optim., 38:2 (2017), 139–159  crossref  mathscinet  zmath  isi  scopus
    252. Dolgopolik M.V., “A Unifying Theory of Exactness of Linear Penalty Functions II: Parametric Penalty Functions”, Optimization, 66:10 (2017), 1577–1622  crossref  mathscinet  zmath  isi  scopus  scopus
    253. Ioffe A.D., “Implicit Functions: a Metric Theory”, Set-Valued Var. Anal., 25:4, 2 (2017), 679–699  crossref  mathscinet  zmath  isi  scopus  scopus
    254. Kruger A.Y., Luke D.R., Thao N.H., “About Subtransversality of Collections of Sets”, Set-Valued Var. Anal., 25:4, 2 (2017), 701–729  crossref  mathscinet  zmath  isi  scopus  scopus
    255. Canovas M.J., Parra J., Ruckmann J.-J., Toledo F.J., “Point-Based Neighborhoods For Sharp Calmness Constants in Linear Programming”, Set-Valued Var. Anal., 25:4, 2 (2017), 757–772  crossref  mathscinet  zmath  isi  scopus  scopus
    256. Bianchi M., Kassay G., Pini R., “Stability of Equilibria Via Regularity of the Diagonal Subdifferential Operator”, Set-Valued Var. Anal., 25:4, 2 (2017), 789–805  crossref  mathscinet  zmath  isi  scopus  scopus
    257. Gusev M.I., Zykov I.V., “On Extremal Properties of Boundary Points of Reachable Sets For a System With Integrally Constrained Control”, IFAC PAPERSONLINE, 50:1 (2017), 4082–4087  crossref  isi  scopus  scopus
    258. Daniilidis A., Drusvyatskiy D., “Sweeping By a Tame Process”, Ann. Inst. Fourier, 67:5 (2017), 2201–2223  crossref  mathscinet  isi  scopus
    259. Adly S., Huynh Van Ngai, Nguyen Van Vu, “Stability of Metric Regularity With Set-Valued Perturbations and Application to Newton'S Method For Solving Generalized Equations”, Set-Valued Var. Anal., 25:3, SI (2017), 543–567  crossref  mathscinet  zmath  isi  scopus
    260. Ye M., Guu S.-M., Peng L., Wang X., “Local Error Bounds For Infinite Convex-Composite Inequalities in Banach Spaces”, J. Nonlinear Convex Anal., 18:6, SI (2017), 1129–1140  mathscinet  zmath  isi
    261. Zheng X.Y., Zhu J., “Stable Well-Posedness and Tilt Stability With Respect to Admissible Functions”, ESAIM-Control OPtim. Calc. Var., 23:4 (2017), 1397–1418  crossref  mathscinet  zmath  isi  scopus
    262. Huang L., Wei Zh., “On Metric Subregularity For Convex Constraint Systems By Primal Equivalent Conditions”, Optim. Lett., 11:8 (2017), 1713–1728  crossref  mathscinet  zmath  isi  scopus
    263. Si Tiep Dinh, Huy Vui Ha, Tien Son Pham, “Holder-Type Global Error Bounds For Non-Degenerate Polynomial Systems”, Acta Math. Vietnam, 42:3 (2017), 563–585  crossref  mathscinet  zmath  isi  scopus
    264. Bao T.Q., Hillmann M., Tammer Ch., “Subdifferentials of Nonlinear Scalarization Functions and Applications”, J. Nonlinear Convex Anal., 18:4, SI (2017), 589–605  mathscinet  isi
    265. Huynh Van Ngai Nguyen Huu Tron Phan Nhat Tinh, “Directional Holder Metric Subregularity and Application to Tangent Cones”, J. Convex Anal., 24:2 (2017), 417–457  mathscinet  zmath  isi
    266. Ioffe A.D., “Transversality in Variational Analysis”, J. Optim. Theory Appl., 174:2 (2017), 343–366  crossref  mathscinet  zmath  isi  scopus
    267. Kruger A.Y., “About Intrinsic Transversality of Pairs of Sets”, Set-Valued Var. Anal., 26:1 (2018), 111–142  crossref  mathscinet  zmath  isi  scopus  scopus
    268. Kruger A.Y., Luke D.R., Thao N.H., “Set Regularities and Feasibility Problems”, Math. Program., 168:1-2, SI (2018), 279–311  crossref  mathscinet  zmath  isi  scopus  scopus
    269. Kruger A.Y., Lopez M.A., Thera M.A., “Perturbation of Error Bounds”, Math. Program., 168:1-2, SI (2018), 533–554  crossref  mathscinet  zmath  isi  scopus  scopus
    270. Wei Zh., Yao J.-Ch., “On Several Types of Basic Constraint Qualifications Via Coderivatives For Generalized Equations”, J. Optim. Theory Appl., 177:1 (2018), 106–126  crossref  mathscinet  zmath  isi  scopus  scopus
    271. Bui H.T., Kruger A.Y., “About Extensions of the Extremal Principle”, Vietnam J. Math., 46:2, 2, SI (2018), 215–242  crossref  mathscinet  zmath  isi  scopus
    272. He Y., Ng K.F., “Stability of P-Order Metric Regularity”, Vietnam J. Math., 46:2, 2, SI (2018), 285–291  crossref  mathscinet  zmath  isi  scopus
    273. Nguyen Hieu Thao, “A Convergent Relaxation of the Douglas-Rachford Algorithm”, Comput. Optim. Appl., 70:3 (2018), 841–863  crossref  mathscinet  zmath  isi  scopus
    274. Adly S., Huynh Van Ngai, Nguyen Van Vu, “Newton-Type Method For Solving Generalized Equations on Riemannian Manifolds”, J. Convex Anal., 25:2, SI (2018), 341–370  mathscinet  zmath  isi
    275. Bianchi M., Kassay G., Pini R., “On a Sufficient Condition For Weak Sharp Efficiency in Multiobjective Optimization”, J. Optim. Theory Appl., 178:1 (2018), 78–93  crossref  mathscinet  isi  scopus
    276. Cibulka R., Dontchev A.L., Kruger A.Y., “Strong Metric Subregularity of Mappings in Variational Analysis and Optimization”, J. Math. Anal. Appl., 457:2 (2018), 1247–1282  crossref  mathscinet  zmath  isi  scopus
    277. Drusvyatskiy D., Lewis A.S., “Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods”, Math. Oper. Res., 43:3 (2018), 919–948  crossref  isi  scopus
    278. Petrusel A., Petrusel G., Yao J.-Ch., “Variational Analysis Concepts in the Theory of Multi-Valued Coincidence Problems”, J. Nonlinear Convex Anal., 19:6 (2018), 935–958  mathscinet  isi
    279. Rashid M.H., “Stability Analysis of Gauss-Type Proximal Point Method For Metrically Regular Mappings”, Cogent Math., 5:1 (2018), 1490161  crossref  isi
    280. Fabian M., Ioffe A.D., Revalski J., “Separable Reduction of Local Metric Regularity”, Proc. Amer. Math. Soc., 146:12 (2018), 5157–5167  crossref  mathscinet  zmath  isi
    281. Canovas M.J., Parra J., Toledo F.J., “Lipschitz Modulus of Fully Perturbed Linear Programs”, Pac. J. Optim., 14:3 (2018), 381–398  mathscinet  isi
    282. Li Ch., Ng K.F., “Quantitative Analysis For Perturbed Abstract Inequality Systems in Banach Spaces”, SIAM J. Optim., 28:4 (2018), 2872–2901  crossref  isi
    283. Canovas M.J., Dinh N., Long D.H., Parra J., “An Approach to Calmness of Linear Inequality Systems From Farkas Lemma”, Optim. Lett., 13:2 (2019), 295–307  crossref  mathscinet  isi  scopus
    284. Petrusel A., Petrusel G., Yao J.-Ch., “Pseudo-Contractivity and Metric Regularity in Fixed Point Theory”, J. Optim. Theory Appl., 180:1, SI (2019), 5–18  crossref  mathscinet  zmath  isi  scopus
    285. Cibulka R. Fabian M. Kruger A.Y., “On Semiregularity of Mappings”, J. Math. Anal. Appl., 473:2 (2019), 811–836  crossref  mathscinet  zmath  isi  scopus
    286. Zhang B., Zheng X., “Well-Posedness and Generalized Metric Subregularity With Respect to An Admissible Function”, Sci. China-Math., 62:4 (2019), 809–822  crossref  mathscinet  isi  scopus
    287. Canovas M.J., Hall J.A.J., Lopez M.A., Parra J., “Calmness of Partially Perturbed Linear Systems With An Application to the Central Path”, Optimization, 68:2-3, SI (2019), 465–483  crossref  mathscinet  zmath  isi  scopus
    288. Penot J.-P., “Error Bounds and Multipliers in Constrained Optimization Problems With Tolerance”, SIAM J. Optim., 29:1 (2019), 522–540  crossref  mathscinet  zmath  isi  scopus
    289. Kassay G. Radulescu V., “Equilibrium Problems and Applications”, Equilibrium Problems and Applications, Mathematics in Science and Engineering, Elsevier Academic Press Inc, 2019, 1–419  isi
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1725
    Full text:459
    First page:2

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019