Geometry of Banach spaces, set-values analysis, optimization.
Main publications:
M. V. Balashov, E. S. Polovinkin. M-silno vypuklye mnozhestva i ikh porozhdayuschie podmnozhestva // Matem. sb. 2000. T. 191. # 1. S. 27–64.
E. S. Polovinikn, M. V. Balashov. Elementy vypuklogo i silno vypuklogo analiza. M., Fizmatlit. 2007. 2-e izd., ispravlennoe i dopolnennoe. 440 s.
Balashov, Maxim V.; Repovs, Dusan, Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order, Journal of Mathematical Analysis and Applications
Volume: 377 Issue: 2, 2011, Pages: 754-761.
Balashov, MV, On the P-property of compact convex sets, Mathematical Notes,
Volume: 71 Issue: 3-4, 2002, Pages: 295-304.
Balashov, Maxim V.,
About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set,
Journal of Convex Analysis,
Volume: 24 Issue: 2, 2017, Pages: 493-500.
M. V. Balashov, K. Z. Biglov, A. A. Tremba, “On some problems with multivalued mappings”, Avtomat. i Telemekh., 2024, no. 5, 58–85
2.
M. V. Balashov, K. Z. Biglov, “The Strong Convexity Supporting Condition and the Lipschitz Condition for the Metric Projection”, Mat. Zametki, 115:2 (2024), 197–207; Math. Notes, 115:2 (2024), 164–172
M. V. Balashov, “Lipschitz continuity of the metric projection operator and convergence of gradient methods”, Mat. Sb., 215:4 (2024), 62–80; Sb. Math., 215:4 (2024), 494–510
M. V. Balashov, A. A. Tremba, “The gradient projection method for a supporting function on the unit sphere and its applications”, Comput. Math. Math. Phys., 64:4 (2024), 676–692
2023
5.
M. V. Balashov, “The Lezanski – Polyak – Lojasiewicz inequality and the convergence of the gradient projection algorithm”, Izv. Saratov Univ. Math. Mech. Inform., 23:1 (2023), 4–10
6.
M. V. Balashov, “Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set”, Mat. Zametki, 113:5 (2023), 655–666; Math. Notes, 113:5 (2023), 632–641
M. V. Balashov, R. A. Kamalov, “Optimization of the reachable set of a linear system with respect to another set”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 739–759; Comput. Math. Math. Phys., 63:5 (2023), 751–770
M. V. Balashov, “Covering a Set by a Convex Compactum: Error Estimates and Computation”, Mat. Zametki, 112:3 (2022), 337–349; Math. Notes, 112:3 (2022), 349–359
M. V. Balashov, “Embedding of a homothete in a convex compactum: an algorithm and its convergence”, Russian Universities Reports. Mathematics, 27:138 (2022), 143–149
M. V. Balashov, “Growth Conditions on a Function and the Error Bound Condition”, Mat. Zametki, 109:4 (2021), 625–630; Math. Notes, 109:4 (2021), 638–643
12.
M. V. Balashov, R. A. Kamalov, “The gradient projection method with Аrmijo's step size on manifolds”, Zh. Vychisl. Mat. Mat. Fiz., 61:11 (2021), 1814–1824; Comput. Math. Math. Phys., 61:11 (2021), 1776–1786
M. V. Balashov, “On the Gradient Projection Method for Weakly Convex Functions on a Proximally Smooth Set”, Mat. Zametki, 108:5 (2020), 657–668; Math. Notes, 108:5 (2020), 643–651
M. V. Balashov, “The gradient projection algorithm for a proximally smooth set and a function with Lipschitz continuous gradient”, Mat. Sb., 211:4 (2020), 3–26; Sb. Math., 211:4 (2020), 481–504
M. V. Balashov, “The Lipschitz property of the metric projection in the Hilbert space”, Fundam. Prikl. Mat., 22:1 (2018), 13–29; J. Math. Sci., 250:3 (2020), 391–403
M. V. Balashov, “Maximization of a function with Lipschitz continuous gradient”, Fundam. Prikl. Mat., 18:5 (2013), 17–25; J. Math. Sci., 209:1 (2015), 12–18
M. V. Balashov, G. E. Ivanov, “Weakly convex and proximally smooth sets in Banach spaces”, Izv. RAN. Ser. Mat., 73:3 (2009), 23–66; Izv. Math., 73:3 (2009), 455–499
M. V. Balashov, I. I. Bogdanov, “Properties of P-sets and Trapped Compact Convex Sets”, Mat. Zametki, 84:4 (2008), 496–505; Math. Notes, 84:4 (2008), 465–472
G. E. Ivanov, M. V. Balashov, “Lipschitz continuous parametrizations of set-valued maps with
weakly convex images”, Izv. RAN. Ser. Mat., 71:6 (2007), 47–68; Izv. Math., 71:6 (2007), 1123–1143
M. V. Balashov, G. E. Ivanov, “Properties of the metric projection on weakly vial-convex sets and parametrization of set-valued mappings with weakly convex images”, Mat. Zametki, 80:4 (2006), 483–489; Math. Notes, 80:4 (2006), 461–467
M. V. Balashov, “An Analog of the Krein–Mil'man Theorem for Strongly Convex Hulls in Hilbert Space”, Mat. Zametki, 71:1 (2002), 37–42; Math. Notes, 71:1 (2002), 34–38
E. S. Polovinkin, G. E. Ivanov, M. V. Balashov, R. V. Konstantinov, A. V. Khorev, “An algorithm for the numerical solution of linear differential games”, Mat. Sb., 192:10 (2001), 95–122; Sb. Math., 192:10 (2001), 1515–1542
M. V. Balashov, O. V. Besov, B. I. Golubov, V. V. Goryainov, V. N. Diesperov, S. I. Dudov, G. E. Ivanov, S. P. Konovalov, R. V. Konstantinov, A. B. Kurzhanskii, S. R. Nasyrov, A. G. Sergeev, V. V. Starkov, V. M. Tikhomirov, M. I. Shabunin, “Evgenii Sergeevich Polovinkin (on his 70th birthday)”, Uspekhi Mat. Nauk, 71:5(431) (2016), 187–190; Russian Math. Surveys, 71:5 (2016), 983–987
2010
32.
M. V. Balashov, I. I. Bogdanov, R. N. Karasev, “Студенческие математические олимпиады МФТИ”, Mat. Pros., Ser. 3, 14 (2010), 214–224
Presentations in Math-Net.Ru
1.
Метрическая проекция в гильбертовом пространстве M. V. Balashov Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics April 24, 2024 16:00
2.
Градиентные методы минимизации M. V. Balashov XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 29, 2024 11:00
About the interior of one set-valued integral M. V. Balashov The ninth international conference "Quasilinear Equations, Inverse Problems and their Applications" (QIPA 2023) December 5, 2023 15:30
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