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Dykhta, Vladimir Aleksandrovich
(1949–2025)
Statistics Math-Net.Ru
Total publications: 38
Scientific articles: 35
Presentations: 3

Number of views:
This page:5855
Abstract pages:17854
Full texts:6287
References:2034
Professor
Doctor of physico-mathematical sciences (1992)
Birth date: 1.10.1949

https://www.mathnet.ru/eng/person29209
https://ru.wikipedia.org/wiki/Dykhta,_Vladimir_Aleksandrovich
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/198676
https://elibrary.ru/author_items.asp?authorid=6186

Publications in Math-Net.Ru Citations
2025
1. V. A. Dykhta, “Feedback minimum principle for optimal control problems with terminal conditions and its extensions”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 241 (2025),  18–29  mathnet
2024
2. V. A. Dykhta, “Support majorants and feedback minimum principles for discrete optimal control problems”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 234 (2024),  43–49  mathnet
2023
3. V. A. Dykhta, “Methods for improving the efficiency of the positional minimum principle in optimal control problems”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 224 (2023),  54–64  mathnet
2022
4. Vladimir A. Dykhta, “Feedback minimum principle: variational strengthening of the concept of extremality in optimal control”, Bulletin of Irkutsk State University. Series Mathematics, 41 (2022),  19–39  mathnet  mathscinet 2
5. V. A. Dykhta, “On the set of necessary optimality conditions with positional controls generated by weakly decreasing solutions of the Hamilton-Jacobi inequality”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:3 (2022),  83–93  mathnet  elib 1
2018
6. V. A. Dykhta, O. N. Samsonyuk, “Feedback minimum principle for impulsive processes”, Bulletin of Irkutsk State University. Series Mathematics, 25 (2018),  46–62  mathnet 1
2017
7. V. A. Dykhta, “Feedback minimum principle for quasi-optimal processes of terminally-constrained control problems”, Bulletin of Irkutsk State University. Series Mathematics, 19 (2017),  113–128  mathnet 2
2015
8. V. A. Dykhta, “Positional strengthenings of the maximum principle and sufficient optimality conditions”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015),  73–86  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 293, suppl. 1 (2016), S43–S57  isi  scopus 19
2014
9. V. A. Dykhta, “Nonstandard duality and nonlocal necessary optimality conditions in nonconvex optimal control problems”, Avtomat. i Telemekh., 2014, no. 11,  19–37  mathnet; Autom. Remote Control, 75:11 (2014), 1906–1921  isi  scopus 17
10. V. A. Dykhta, “Weakly monotone solutions of the Hamilton–Jacobi inequality and optimality conditions with positional controls”, Avtomat. i Telemekh., 2014, no. 5,  31–49  mathnet; Autom. Remote Control, 75:5 (2014), 829–844  isi  scopus 18
11. V. A. Dykhta, “Variational Optimality Conditions with Feedback Descent Controls that Strengthen the Maximum Principle”, Bulletin of Irkutsk State University. Series Mathematics, 8 (2014),  86–103  mathnet 3
2011
12. V. A. Dykhta, S. P. Sorokin, “Hamilton–Jacobi inequalities and the optimality conditions in the problems of control with common end constraints”, Avtomat. i Telemekh., 2011, no. 9,  13–27  mathnet  mathscinet  zmath; Autom. Remote Control, 72:9 (2011), 1808–1821  isi  scopus 4
13. V. A. Dykhta, S. P. Sorokin, “Positional solutions of Hamilton–Jacobi equations in control problems for discrete-continuous systems”, Avtomat. i Telemekh., 2011, no. 6,  48–63  mathnet  mathscinet  zmath; Autom. Remote Control, 72:6 (2011), 1184–1198  isi  scopus 3
14. V. A. Dykhta, O. N. Samsonyuk, “The canonical theory of the impulse process optimality”, CMFD, 42 (2011),  118–124  mathnet  mathscinet; Journal of Mathematical Sciences, 199:6 (2014), 646–653  scopus 5
15. V. M. Aleksandrov, V. A. Dykhta, “Approximate solution to the resource consumption minimization problem. II. Estimates for the proximity of controls”, Sib. Zh. Ind. Mat., 14:3 (2011),  3–13  mathnet  mathscinet; J. Appl. Industr. Math., 6:2 (2012), 135–144 2
16. V. M. Aleksandrov, V. A. Dykhta, “Approximate solution to the resource consumption minimization problem. I. Construction of a quasioptimal control”, Sib. Zh. Ind. Mat., 14:2 (2011),  3–14  mathnet  mathscinet; J. Appl. Industr. Math., 5:4 (2011), 467–477 1
2010
17. V. A. Dykhta, “Analysis of sufficient optimality conditions with a set of Lyapunov type functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010),  66–75  mathnet  elib 5
18. V. A. Dykhta, O. N. Samsonyuk, “Hamilton–Jacobi inequalities in control problems for impulsive dynamical systems”, Trudy Mat. Inst. Steklova, 271 (2010),  93–110  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 271 (2010), 86–102  isi  elib  scopus 6
2009
19. A. V. Arguchintsev, V. A. Dykhta, V. A. Srochko, “Optimal control: nonlocal conditions, computational methods, and the variational principle of maximum”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 1,  3–43  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 53:1 (2009), 1–35 41
20. V. A. Dykhta, O. N. Samsonyuk, “A maximum principle for smooth optimal impulsive control problems with multipoint state constraints”, Zh. Vychisl. Mat. Mat. Fiz., 49:6 (2009),  981–997  mathnet  zmath; Comput. Math. Math. Phys., 49:6 (2009), 942–957  isi  scopus 21
2006
21. V. A. Dykhta, “Lyapunov–Krotov inequality and sufficient conditions in optimal control”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 110 (2006),  76–108  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 121:2 (2004), 2156–2177 20
2002
22. V. A. Dykhta, “A Variational Maximum Principle for Classical Optimal Control Problems”, Avtomat. i Telemekh., 2002, no. 4,  47–54  mathnet  mathscinet  zmath; Autom. Remote Control, 63:4 (2002), 560–567  isi  scopus 1
23. N. V. Antipina, V. A. Dykhta, “Linear Lyapunov–Krotov functions and sufficient conditions for optimality in the form of the maximum principle”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 12,  11–22  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 46:12 (2002), 9–20 17
2001
24. V. A. Dykhta, N. V. Derenko, “Numerical methods for solving problems of optimal impulse control that are based on the variational maximum principle”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 12,  32–40  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 45:12 (2001), 29–37
25. V. A. Dykhta, O. N. Samsonyuk, “The maximum principle in nonsmooth optimal impulse control problems with multipoint phase constraints”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 2,  19–32  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 45:2 (2001), 16–29 2
1999
26. V. A. Dykhta, “Impulsive optimal control in models of economics and quantum electronics”, Avtomat. i Telemekh., 1999, no. 11,  100–112  mathnet  mathscinet  zmath; Autom. Remote Control, 60:11 (1999), 1603–1613  isi 9
27. V. A. Dykhta, O. N. Samsonyuk, “The maximum principle in nonsmooth optimal control problems with discontinuous trajectories”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 12,  26–37  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 43:12 (1999), 23–34 2
1996
28. V. A. Dykhta, “Necessary conditions for the optimality of impulse processes with constraints on the image of the control measure”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 12,  9–16  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:12 (1996), 7–13 6
1994
29. V. A. Dykhta, “The variational maximum principle and second-order optimality conditions for impulse processes and singular processes”, Sibirsk. Mat. Zh., 35:1 (1994),  70–82  mathnet  mathscinet  zmath; Siberian Math. J., 35:1 (1994), 65–76  isi 26
1991
30. V. A. Dykhta, “A variational maximum principle for pulse and singular regimes in an optimization problem that is linear with respect to control”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 11,  89–91  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:11 (1991), 89–91 1
1983
31. V. A. Dykhta, G. A. Kolokol'nikova, “Minimum conditions on the set of sequences in a degenerate variational problem”, Mat. Zametki, 34:5 (1983),  735–744  mathnet  mathscinet; Math. Notes, 34:5 (1983), 859–863  isi 5
1981
32. V. A. Dykhta, “Conditions of loca*l minimum for singular modes in systems with linear control”, Avtomat. i Telemekh., 1981, no. 12,  5–10  mathnet  mathscinet  zmath; Autom. Remote Control, 42:12 (1981), 1583–1587 2
1979
33. V. A. Dykhta, “Singular modes of a nonlinear system in the case of multiple maxima”, Avtomat. i Telemekh., 1979, no. 2,  16–19  mathnet  mathscinet  zmath; Autom. Remote Control, 40:2 (1979), 166–168
1977
34. V. I. Gurman, V. A. Dykhta, “Singular problems of optimal control and the method of multiple maxima”, Avtomat. i Telemekh., 1977, no. 3,  51–59  mathnet  mathscinet  zmath; Autom. Remote Control, 38:3 (1977), 343–350 4
1976
35. V. I. Gurman, V. A. Dykhta, “Sufficient conditions for a strong minimum for degenerate optimal control problems”, Differ. Uravn., 12:12 (1976),  2129–2138  mathnet  mathscinet  zmath
2025
36. I. V. Bychkov, V. A. Dykhta, A. L. Kazakov, N. I. Pogodaev, V. A. Shelekhov, “On the 85th birthday anniversary of the RAS Corresponding Member, professor A. A. Tolstonogov”, Bulletin of Irkutsk State University. Series Mathematics, 51 (2025),  167–178  mathnet
2017
37. V. A. Dykhta, “Scientific achievements of professor V. I. Gurman”, Bulletin of Irkutsk State University. Series Mathematics, 19 (2017),  6–21  mathnet
38. A. V. Arguchintsev, I. V. Bychkov, V. A. Baturin, V. A. Dykhta, G. A. Shishkin, “In Memory of Professor Vladimir Iosifovich Gurman (1934–2016)”, Bulletin of Irkutsk State University. Series Mathematics, 19 (2017),  1–5  mathnet

Presentations in Math-Net.Ru
1. On variational necessary optimality conditions with descent feedback controls strengthening the maximum principle
V. A. Dykhta
International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko
June 9, 2022 12:00   
2. Quadratic supersolutions of Hamilton-Jacobi equations and second order feedback minimum principle
V. A. Dykhta
Optimization and nonlinear analysis
May 27, 2021 14:00   
3. Позиционный принцип минимума в задачах оптимального управления
V. A. Dykhta
Geometric Theory of Optimal Control
December 2, 2020 15:00   

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