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Zh. Vychisl. Mat. Mat. Fiz., 1965, Volume 5, Number 3, Pages 395–453 (Mi zvmmf7583)  

This article is cited in 52 scientific papers (total in 52 papers)

Extremum problems in the presence of restrictions

A. Ya. Dubovitskii, A. A. Milyutin

Moscow

Full text: PDF file (6591 kB)

English version:
USSR Computational Mathematics and Mathematical Physics, 1965, 5:3, 1–80

Bibliographic databases:

UDC: 519.31/.33
Received: 04.05.1964

Citation: A. Ya. Dubovitskii, A. A. Milyutin, “Extremum problems in the presence of restrictions”, Zh. Vychisl. Mat. Mat. Fiz., 5:3 (1965), 395–453; U.S.S.R. Comput. Math. Math. Phys., 5:3 (1965), 1–80

Citation in format AMSBIB
\Bibitem{DubMil65}
\by A.~Ya.~Dubovitskii, A.~A.~Milyutin
\paper Extremum problems in the presence of restrictions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1965
\vol 5
\issue 3
\pages 395--453
\mathnet{http://mi.mathnet.ru/zvmmf7583}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0191691}
\zmath{https://zbmath.org/?q=an:0158.33504}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1965
\vol 5
\issue 3
\pages 1--80
\crossref{https://doi.org/10.1016/0041-5553(65)90148-5}


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    This publication is cited in the following articles:
    1. A. D. Ioffe, V. M. Tikhomirov, “Duality of convex functions and extremum problems”, Russian Math. Surveys, 23:6 (1968), 53–124  mathnet  crossref  mathscinet  zmath
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    4. V. L. Levin, “O subdifferentsialakh vypuklykh funktsionalov”, UMN, 25:4(154) (1970), 183–184  mathnet  mathscinet  zmath
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    6. G. Sh. Rubinshtein, “Duality in mathematical programming and some problems of convex analysis”, Russian Math. Surveys, 25:5 (1970), 171–200  mathnet  crossref  mathscinet  zmath
    7. V. F. Dem'yanov, V. N. Malozemov, “On the theory of non-linear minimax problems”, Russian Math. Surveys, 26:3 (1971), 57–115  mathnet  crossref  mathscinet  zmath
    8. V. I. Arkin, V. L. Levin, “Convexity of values of vector integrals, theorems on measurable choice and variational problems”, Russian Math. Surveys, 27:3 (1972), 21–85  mathnet  crossref  mathscinet  zmath
    9. V. G. Boltyanskii, “The method of tents in the theory of extremal problems”, Russian Math. Surveys, 30:3 (1975), 1–54  mathnet  crossref  mathscinet  zmath
    10. A. Ya. Dubovitskii, “Solution of a problem of S. Ulam on optimal matching of segments”, Math. USSR-Izv., 10:3 (1976), 639–651  mathnet  crossref  mathscinet  zmath
    11. A. V. Dmitruk, “Application of sliding mode method to optimal control problems with mixed constraints”, Funct. Anal. Appl., 10:3 (1976), 197–201  mathnet  crossref  mathscinet  zmath
    12. Yu. I. Brodskii, “Necessary conditions for a weak extremum in optimal control problems on an infinite time interval”, Math. USSR-Sb., 34:3 (1978), 327–343  mathnet  crossref  mathscinet  zmath
    13. V. M. Safro, “Extremum conditions for minimax problems”, Russian Math. Surveys, 33:2 (1978), 245–246  mathnet  crossref  mathscinet  zmath
    14. E. S. Levitin, A. A. Milyutin, N. P. Osmolovskii, “Conditions of high order for a local minimum in problems with constraints”, Russian Math. Surveys, 33:6 (1978), 97–168  mathnet  crossref  mathscinet  zmath
    15. S. S. Kutateladze, “Convex operators”, Russian Math. Surveys, 34:1 (1979), 181–214  mathnet  crossref  mathscinet  zmath
    16. 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
    17. A. Ya. Dubovitskii, V. A. Dubovitskii, “Necessary conditions for a strong minimum in optimal control problems with degeneracy of the end-point and phase constraints”, Russian Math. Surveys, 40:2 (1985), 209–210  mathnet  crossref  zmath  adsnasa  isi
    18. V. I. Kazimirov, V. I. Plotnikov, I. M. Starobinets, “An abstract scheme for the method of variations and necessary conditions for an extremum”, Math. USSR-Izv., 26:1 (1986), 133–151  mathnet  crossref  mathscinet
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    21. A. N. Tikhonov (jr.), A. V. Tikhonravov, M. K. Trubetskov, “Second-order optimization methods in the synthesis of multilayer coatings”, Comput. Math. Math. Phys., 33:10 (1993), 1339–1352  mathnet  mathscinet  zmath  isi
    22. S. M. Aseev, “A method of smooth approximation in the theory of necessary optimality conditions for differential inclusions”, Izv. Math., 61:2 (1997), 235–258  mathnet  crossref  crossref  mathscinet  zmath  isi
    23. V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions”, Izv. Math., 62:4 (1998), 807–832  mathnet  crossref  crossref  mathscinet  zmath  isi
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    25. S. M. Aseev, “Extremal Problems for Differential Inclusions with State Constraints”, Proc. Steklov Inst. Math., 233 (2001), 1–63  mathnet  mathscinet  zmath
    26. 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
    27. V. N. Baranov, “Zadachi vyzhivaniya dlya sistem s posledeistviem”, Izv. IMI UdGU, 2003, no. 2(28), 3–102  mathnet
    28. R. Gabasov, N. M. Dmitruk, F. M. Kirillova, “The indirect optimal control of dynamical systems”, Comput. Math. Math. Phys., 44:3 (2004), 418–439  mathnet  mathscinet  zmath
    29. Gorbunov V., Lutoshkin I., “Development and Experience of Using the Parameterization Method in Singular Problems of Dynamic Optimization”, J. Comput. Syst. Sci. Int., 43:5 (2004), 725–742  isi
    30. V. M. Tikhomirov, “Gladko-approksimativno-vypuklyi printsip i ego prilozheniya”, Vladikavk. matem. zhurn., 7:4 (2005), 52–66  mathnet  mathscinet
    31. V. Yu. Tertychny-Dauri, “Variational dynamic problems with parameters and their adaptive interpretation”, Autom. Remote Control, 66:9 (2005), 1465–1477  mathnet  crossref  mathscinet
    32. V. V. Gorokhovik, “Kasatelnye vektory vtorogo poryadka k mnozhestvam i usloviya minimalnosti dlya tochek podmnozhestv uporyadochennykh normirovannykh prostranstv”, Tr. In-ta matem., 14:2 (2006), 35–47  mathnet
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    36. M. Sh. Misrikhanov, V. N. Ryabchenko, “Matrix sign function in the problems of analysis and design of the linear systems”, Autom. Remote Control, 69:2 (2008), 198–222  mathnet  crossref  mathscinet  zmath  isi
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    38. A. M. Tsirlin, “Optimality conditions of sliding modes and the maximum principle for control problems with the scalar argument”, Autom. Remote Control, 70:5 (2009), 839–854  mathnet  crossref  mathscinet  zmath  isi
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    41. N. Yu. Troshina, C. V. Troshina, “Primenenie printsipa maksimuma Pontryagina k optimizatsionnym modelyam ekonomiki”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:3(2) (2011), 52–63  mathnet  crossref
    42. Verenikin A.O., “Potentsial ekonomicheskogo ravnovesiya”, Vestnik Moskovskogo universiteta. Seriya 6: Ekonomika, 2011, no. 5, 3–26  elib
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    45. K. S. Musabekov, “The Method of Penalty Function in One Problem of Optimal Control with Phase Constraint”, J. Math. Sci., 203:4 (2014), 558–569  mathnet  crossref
    46. A. D. Ioffe, “On necessary conditions for a minimum”, J. Math. Sci., 217:6 (2016), 751–772  mathnet  crossref  mathscinet
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    48. S. M. Aseev, “Optimizatsiya dinamiki upravlyaemoi sistemy pri nalichii faktorov riska”, Tr. IMM UrO RAN, 23:1 (2017), 27–42  mathnet  crossref  mathscinet  elib
    49. Dmitruk A., Samylovskiy I., “On the Relation Between Two Approaches to Necessary Optimality Conditions in Problems With State Constraints”, J. Optim. Theory Appl., 173:2 (2017), 391–420  crossref  isi
    50. A. V. Dmitruk, N. P. Osmolovskii, “Variations of the $v$-change of time in problems with state constraints”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S49–S64  mathnet  crossref  crossref  isi  elib
    51. G. L. Karaseva, E. A. Ruzhitskaya, “Metod resheniya spetsialnoi zadachi optimalnogo upravleniya s fazovymi ogranicheniyami”, PFMT, 2018, no. 4(37), 80–84  mathnet
    52. Samylovskiy I.A., “On One Method to Obtain Stationarity Conditions For An Optimal Control Problem Trajectory With a Smooth Boundary Contact”, IFAC PAPERSONLINE, 51:32 (2018), 384–388  crossref  isi
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