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Uspekhi Mat. Nauk, 1978, Volume 33, Issue 6(204), Pages 85–148 (Mi umn3585)  

This article is cited in 40 scientific papers (total in 40 papers)

Conditions of high order for a local minimum in problems with constraints

E. S. Levitin, A. A. Milyutin, N. P. Osmolovskii


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English version:
Russian Mathematical Surveys, 1978, 33:6, 97–168

Bibliographic databases:

UDC: 517.5
MSC: 49Kxx, 49J40
Received: 23.01.1978

Citation: E. S. Levitin, A. A. Milyutin, N. P. Osmolovskii, “Conditions of high order for a local minimum in problems with constraints”, Uspekhi Mat. Nauk, 33:6(204) (1978), 85–148; Russian Math. Surveys, 33:6 (1978), 97–168

Citation in format AMSBIB
\Bibitem{LevMilOsm78}
\by E.~S.~Levitin, A.~A.~Milyutin, N.~P.~Osmolovskii
\paper Conditions of~high order for~a~local minimum in~problems with constraints
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 6(204)
\pages 85--148
\mathnet{http://mi.mathnet.ru/umn3585}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=526013}
\zmath{https://zbmath.org/?q=an:0456.49015|0409.49016}
\transl
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 6
\pages 97--168
\crossref{https://doi.org/10.1070/RM1978v033n06ABEH003885}


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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. A. V. Dmitruk, A. A. Milyutin, N. P. Osmolovskii, “Lyusternik's theorem and the theory of extrema”, Russian Math. Surveys, 35:6 (1980), 11–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. V. Dmitruk, “A condition of Jacobi type for a quadratic form to be nonnegative on a finite-faced cone”, Math. USSR-Izv., 18:3 (1982), 525–535  mathnet  crossref  mathscinet  zmath
    3. A. V. Arutyunov, N. T. Tynyanskii, “First- and second-order conditions in the problem of optimal high-speed”, Russian Math. Surveys, 36:6 (1981), 167–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. N. T. Tynyanskii, A. V. Arutyunov, “On the system of Jacobi equations in a time-optimal problem”, Math. USSR-Izv., 21:2 (1983), 375–397  mathnet  crossref  mathscinet  zmath
    5. V. A. Dubovitskii, “Necessary and sufficient conditions for a Pontryagin minimum in problems of optimal control with singular conditions and generalized controls”, Russian Math. Surveys, 37:3 (1982), 202–203  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. V. Dmitruk, “Quadratic conditions for a Pontryagin minimum in an optimum control problem linear in the control. I: A decoding theorem”, Math. USSR-Izv., 28:2 (1987), 275–303  mathnet  crossref  mathscinet  zmath
    7. A. V. Dmitruk, “Quadratic conditions for a Pontryagin minimum in an optimal control problem linear in the control. II. Theorems on weakening equality constraints”, Math. USSR-Izv., 31:1 (1988), 121–141  mathnet  crossref  mathscinet  zmath
    8. A.D. Ioffe, “On the local surjection property”, Nonlinear Analysis: Theory, Methods & Applications, 11:5 (1987), 565  crossref
    9. M. F. Sukhinin, “Lower semi-Taylor mappings and sufficient conditions for an extremum”, Math. USSR-Sb., 73:1 (1992), 257–271  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. Alexander Ioffe, “On Sensitivity Analysis of Nonlinear Programs in Banach Spaces: The Approach via Composite Unconstrained Optimization”, SIAM J Optim, 4:1 (1994), 1  crossref  mathscinet  isi
    11. U. Ledzewicz, H. Schaettler, “Second-order conditions for extremum problems with nonregular equality constraints”, J Optim Theory Appl, 86:1 (1995), 113  crossref  mathscinet  zmath  isi
    12. Richard F. Hartl, Suresh P. Sethi, Raymond G. Vickson, “A Survey of the Maximum Principles for Optimal Control Problems with State Constraints”, SIAM Rev, 37:2 (1995), 181  crossref  mathscinet  zmath  isi
    13. A. V. Arutyunov, “Second-order conditions in extremal problems with finite-dimensional range. 2-normal maps”, Izv. Math., 60:1 (1996), 39–65  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. Urszula Ledzewicz, Heinz Schättler, “High-order tangent cones and their application in optimization”, Nonlinear Analysis: Theory, Methods & Applications, 30:4 (1997), 2449  crossref
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    20. N. V. Antipina, V. A. Dykhta, “Linear Lyapunov–Krotov functions and sufficient conditions for optimality in the form of the maximum principle”, Russian Math. (Iz. VUZ), 46:12 (2002), 9–20  mathnet  mathscinet  zmath  elib
    21. 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
    22. A. S. Matveev, “Theory of optimal control in the works of V. A. Yakubovich”, Autom. Remote Control, 67:10 (2006), 1645–1698  mathnet  crossref  mathscinet  zmath
    23. Helmut Gfrerer, “Second-Order Necessary Conditions for Nonlinear Optimization Problems with Abstract Constraints: The Degenerate Case”, SIAM J Optim, 18:2 (2007), 589  crossref  mathscinet  zmath  isi  elib
    24. E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Necessary Conditions for an Extremum in a Mathematical Programming Problem”, Proc. Steklov Inst. Math., 256 (2007), 2–25  mathnet  crossref  mathscinet  zmath  elib  elib
    25. R. Andreani, J. M. Martinez, M. L. Schuverdt, “On second-order optimality conditions for nonlinear programming”, Gopt, 56:5 (2007), 529  crossref
    26. Javier F. Rosenblueth, “A direct approach to second order conditions for mixed equality constraints”, Journal of Mathematical Analysis and Applications, 333:2 (2007), 770  crossref
    27. V. F. Borisov, “Kelley condition and structure of Lagrange manifold in a neighborhood of a first-order singular extremal”, Journal of Mathematical Sciences (New York), 151:6 (2008), 3431  crossref  mathscinet  zmath  elib
    28. R. Andreani, E. G. Birgin, J. M. Martínez, M. L. Schuverdt, “Second-order negative-curvature methods for box-constrained and general constrained optimization”, Comput Optim Applic, 2009  crossref  mathscinet  isi
    29. A. V. Arguchintsev, V. A. Dykhta, V. A. Srochko, “Optimal control: nonlocal conditions, computational methods, and the variational principle of maximum”, Russian Math. (Iz. VUZ), 53:1 (2009), 1–35  mathnet  crossref  mathscinet  zmath  elib
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