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Zh. Vychisl. Mat. Mat. Fiz., 1997, Volume 37, Number 11, Pages 1327–1339 (Mi zvmmf1993)  

This article is cited in 41 scientific papers (total in 41 papers)

Equilibrium programming: Proximal methods

A. S. Antipin


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English version:
Computational Mathematics and Mathematical Physics, 1997, 37:11, 1285–1296

Bibliographic databases:
UDC: 519.853.6
MSC: Primary 90C30; Secondary 91B50
Received: 01.04.1996

Citation: A. S. Antipin, “Equilibrium programming: Proximal methods”, Zh. Vychisl. Mat. Mat. Fiz., 37:11 (1997), 1327–1339; Comput. Math. Math. Phys., 37:11 (1997), 1285–1296

Citation in format AMSBIB
\by A.~S.~Antipin
\paper Equilibrium programming: Proximal methods
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1997
\vol 37
\issue 11
\pages 1327--1339
\jour Comput. Math. Math. Phys.
\yr 1997
\vol 37
\issue 11
\pages 1285--1296

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Antipin A.S., “A differential linearization method in equilibrium programming”, Differ Equ, 34:11 (1998), 1445–1458  mathnet  mathscinet  zmath  isi
    2. A. S. Antipin, F. P. Vasil'ev, “A stabilization method for equilibrium programming problems with an approximately given set”, Comput. Math. Math. Phys., 39:11 (1999), 1707–1714  mathnet  mathscinet  zmath
    3. Antipin A., Vasil'ev F., “Regularization method for equilibrium programming problem with inaccurate initial data”, Ill-Posed Variational Problems and Regularization Techniques, Lecture Notes in Economics and Mathematical Systems, 477, 1999, 1–23  crossref  mathscinet  zmath  isi
    4. Antipin A.S., “Second-order controlled differential gradient methods for equilibrium problems”, Differ Equ, 35:5 (1999), 592–601  mathnet  mathscinet  zmath  isi
    5. I. V. Konnov, “Approximate methods for direct-dual variational inequalities of mixed type”, Russian Math. (Iz. VUZ), 44:11 (2000), 53–64  mathnet  mathscinet  zmath
    6. A. S. Antipin, “Solution methods for variational inequalities with coupled constraints”, Comput. Math. Math. Phys., 40:9 (2000), 1239–1254  mathnet  mathscinet  zmath
    7. I. V. Konnov, “The Lagrange multiplier technique for variational inequalities”, Comput. Math. Math. Phys., 41:9 (2001), 1279–1291  mathnet  mathscinet  zmath
    8. A. S. Antipin, F. P. Vasil'ev, “A residual method for equilibrium problems with an inexcactly specified set”, Comput. Math. Math. Phys., 41:1 (2001), 1–6  mathnet  mathscinet  zmath
    9. Konnov I.V., “The method of multipliers for nonlinearly constrained variational inequalities”, Optimization, 51:6 (2002), 907–926  crossref  mathscinet  zmath  isi  scopus
    10. A. S. Antipin, F. P. Vasil'ev, “Regularization methods, based on the extension of a set, for solving an equilibrium programming problem with inexact input data”, Comput. Math. Math. Phys., 42:8 (2002), 1115–1122  mathnet  mathscinet  zmath
    11. F. P. Vasil'ev, A. S. Stukalov, “Approximation of an equilibrium problem with respect to the argument”, Comput. Math. Math. Phys., 44:11 (2004), 1875–1884  mathnet  mathscinet  zmath
    12. F. P. Vasil'ev, A. S. Stukalov, “Conditions for the approximation of equilibrium problems from the value of a functional”, Comput. Math. Math. Phys., 44:7 (2004), 1132–1144  mathnet  mathscinet  zmath
    13. A. S. Stukalov, “A regularized extragradient method for solving equilibrium programming problems in a Hilbert space”, Comput. Math. Math. Phys., 45:9 (2005), 1483–1499  mathnet  mathscinet  zmath
    14. A. S. Antipin, “Extraproximal approach to calculating equilibriums in pure exchange models”, Comput. Math. Math. Phys., 46:10 (2006), 1687–1698  mathnet  crossref  mathscinet
    15. A. S. Stukalov, “An extraproximal method for solving equilibrium programming problems in a Hilbert space”, Comput. Math. Math. Phys., 46:5 (2006), 743–761  mathnet  crossref  mathscinet
    16. Konnov L., “Splitting-type method for systems of variational inequalities”, Computers & Operations Research, 33:2 (2006), 520–534  crossref  mathscinet  zmath  isi  scopus
    17. A. S. Antipin, “Multicriteria equilibrium programming: Extraproximal methods”, Comput. Math. Math. Phys., 47:12 (2007), 1912–1927  mathnet  crossref  mathscinet
    18. A. V. Zykina, “Inverse complementarity in a resource deficit model”, Comput. Math. Math. Phys., 48:11 (2008), 1971–1980  mathnet  crossref  mathscinet  isi
    19. Antipin A., “Multicriteria equilibrium programming problems and methods for their solutions”, Optimization, 58:7 (2009), 729–753  crossref  mathscinet  zmath  isi  elib  scopus
    20. Nguyen Buong, Dang Thi Hai Ha, “Tikhonov Regularization Method for a System of Equilibrium Problems in Banach Spaces”, Ukrainian Math J, 61:8 (2009), 1302–1310  crossref  mathscinet  zmath  isi  scopus
    21. Iusem A.N., Nasri M., “Augmented Lagrangian Methods for Variational Inequality Problems”, Rairo-Operations Research, 44:1 (2010), 5–25  crossref  mathscinet  zmath  isi  scopus
    22. Iusem A.N., Sosa W., “On the proximal point method for equilibrium problems in Hilbert spaces”, Optimization, 59:8 (2010), 1259–1274  crossref  mathscinet  zmath  isi  elib  scopus
    23. A. S. Antipin, E. V. Khoroshilova, “O metodakh ekstragradientnogo tipa dlya resheniya zadachi optimalnogo upravleniya s lineinymi ogranicheniyami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 3:3 (2010), 2–20  mathnet
    24. Wang L., Shan F., Zhang L., “An implementable augmented Lagrange method for solving fixed point problems with coupled constraints”, Nonlinear Analysis-Theory Methods & Applications, 74:5 (2011), 1761–1768  crossref  mathscinet  zmath  isi  scopus
    25. Nguyen Buong, Nguyen Dinh Duong, “A Method for a Solution of Equilibrium Problem and Fixed Point Problem of a Nonexpansive Semigroup in Hilbert's Spaces”, Fixed Point Theory Appl, 2011, 208434  mathscinet  zmath  isi
    26. A. S. Antipin, “Metod modifitsirovannoi funktsii Lagranzha dlya zadach optimalnogo upravleniya so svobodnym pravym kontsom”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:2 (2011), 27–44  mathnet
    27. E. V. Khoroshilova, “Extragradient method of optimal control with terminal constraints”, Autom. Remote Control, 73:3 (2012), 517–531  mathnet  crossref  isi
    28. Mashreghi J., Nasri M., “A proximal augmented Lagrangian method for equilibrium problems”, Appl Anal, 91:1 (2012), 157–172  crossref  mathscinet  zmath  isi  elib  scopus
    29. Antipin A., “Two-Person Game with Nash Equilibrium in Optimal Control Problems”, Optim. Lett., 6:7, SI (2012), 1349–1378  crossref  mathscinet  zmath  isi  elib  scopus
    30. Mashreghi J., Nasri M., “Hybrid Lagrange Multiplier Approaches for Solving Infinite Dimensional Equilibrium Problems with Cone Constraints”, J. Nonlinear Convex Anal., 13:2 (2012), 331–349  mathscinet  zmath  isi  elib
    31. Chbani Z., Riahi H., “Weak and Strong Convergence of an Inertial Proximal Method for Solving Ky Fan Minimax Inequalities”, Optim. Lett., 7:1 (2013), 185–206  crossref  mathscinet  zmath  isi  elib  scopus
    32. Bigi G. Castellani M. Pappalardo M. Passacantando M., “Existence and Solution Methods for Equilibria”, Eur. J. Oper. Res., 227:1 (2013), 1–11  crossref  mathscinet  zmath  isi  elib  scopus
    33. Kim J.K., Nguyen Buong, “A New Iterative Method for Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonself Strictly Pseudocontractive Mappings”, Fixed Point Theory Appl., 2013, 286  crossref  mathscinet  isi  elib  scopus
    34. B. A. Budak, “Shooting method for solving equilibrium programming problems”, Comput. Math. Math. Phys., 53:12 (2013), 1819–1824  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    35. S. R. Aleeva, E. O. Yakubovich, “Ravnovesnoe programmirovanie i ego primenenie dlya nakhozhdeniya ravnovesiya po Neshu”, Vestnik ChelGU, 2013, no. 16, 6–20  mathnet
    36. Kim J.K., Nguyen Buong, Sim J.Yu., “A New Iterative Method For the Set of Solutions of Equilibrium Problems and of Operator Equations With Inverse-Strongly Monotone Mappings”, Abstract Appl. Anal., 2014, 595673  crossref  mathscinet  isi  scopus
    37. A. S. Antipin, O. O. Vasilieva, “Dynamic method of multipliers in terminal control”, Comput. Math. Math. Phys., 55:5 (2015), 766–787  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    38. N. Mijailović, M. Jaćimović, “A proximal method for solving quasi-variational inequalities”, Comput. Math. Math. Phys., 55:12 (2015), 1981–1985  mathnet  crossref  crossref  mathscinet  isi  elib
    39. Antipin A. Khoroshilova E., “On Methods of Terminal Control With Boundary-Value Problems: Lagrange Approach”, Optimization and Its Applications in Control and Data Sciences: in Honor of Boris T. Polyak'S 80Th Birthday, Springer Optimization and Its Applications, 115, ed. Goldengorin B., Springer International Publishing Ag, 2016, 17–49  crossref  mathscinet  zmath  isi  scopus
    40. Lyashko S.I. Semenov V.V., “A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming”, Optimization and Its Applications in Control and Data Sciences: in Honor of Boris T. Polyak'S 80Th Birthday, Springer Optimization and Its Applications, 115, ed. Goldengorin B., Springer International Publishing Ag, 2016, 315–325  crossref  mathscinet  zmath  isi  scopus
    41. F. S. Stonyakin, “Ob adaptivnom proksimalnom metode dlya nekotorogo klassa variatsionnykh neravenstv i smezhnykh zadach”, Tr. IMM UrO RAN, 25, no. 2, 2019, 185–197  mathnet  crossref  elib
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