Edit Profile (opens in new tab) Balashov, Maxim Viktorovich Co-Author Distance Author ID: balashov.maxim-viktorovich Published as: Balashov, M. V.; Balashov, Maxim V.; Balashov, Maksim Viktorovich; Balashov, Maxim Viktorovich more...less Documents Indexed: 57 Publications since 2000, including 1 Book Co-Authors: 22 Co-Authors with 26 Joint Publications 990 Co-Co-Authors all top 5 Co-Authors 31 single-authored 7 Ivanov, Grigorii E. 6 Repovš, Dušan D. 4 Tremba, Andrey Aleksandrovich 3 Biglov, Kamil Z. 3 Polovinkin, Evgenii Sergeevich 2 Golubev, Maxim O. 2 Kamalov, Rinat A. 2 Konstantinov, R. V. 1 Besov, Oleg Vladimirovich 1 Bogdanov, Ilya I. 1 Diesperov, V. N. 1 Golubov, D. I. 1 Goryainov, Viktor V. 1 Khorev, A. V. 1 Konovalov, Sergeĭ Petrovich 1 Kurzhanskiĭ, Aleksandr Borisovich 1 Nasyrov, Semen R. 1 Polyak, Boris Teodorovich 1 Sergeev, Armen Glebovich 1 Shabunin, M. I. 1 Starkov, Victor V. 1 Tikhomirov, Vladimir Mikhaĭlovich all top 5 Serials 12 Journal of Convex Analysis 11 Mathematical Notes 7 Journal of Mathematical Analysis and Applications 6 Computational Mathematics and Mathematical Physics 6 Sbornik: Mathematics 2 Journal of Mathematical Sciences (New York) 2 Izvestiya: Mathematics 2 Set-Valued and Variational Analysis 1 Russian Mathematical Surveys 1 Numerical Functional Analysis and Optimization 1 Optimization 1 Automation and Remote Control 1 Differential Equations 1 Optimization Letters 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 Vestnik Rossiĭskikh Universitetov. Matematika all top 5 Fields 24 Functional analysis (46-XX) 24 Operations research, mathematical programming (90-XX) 23 Convex and discrete geometry (52-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 9 Real functions (26-XX) 8 Approximations and expansions (41-XX) 6 Operator theory (47-XX) 5 Numerical analysis (65-XX) 4 General topology (54-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Systems theory; control (93-XX) 2 Measure and integration (28-XX) 2 Ordinary differential equations (34-XX) 1 History and biography (01-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 45 Publications have been cited 387 times in 202 Documents Cited by ▼ Year ▼ Elements of convex and strongly convex analysis. 2nd ed. (Элементы выпуклого и силпно выпуклого анализа.) Zbl 1181.26028 Polovinkin, E. S.; Balashov, M. V. 81 2007 \(M\)-strongly convex subsets and their generating sets. Zbl 1004.46014 Balashov, M. V.; Polovinkin, E. S. 42 2000 Weakly convex and proximally smooth sets in Banach spaces. Zbl 1179.46013 Balashov, M. V.; Ivanov, G. E. 31 2009 Gradient projection and conditional gradient methods for constrained nonconvex minimization. Zbl 1437.49024 Balashov, M. V.; Polyak, B. T.; Tremba, A. A. 23 2020 About the gradient projection algorithm for a strongly convex function and a proximally smooth set. Zbl 1375.46056 Balashov, Maxim V. 16 2017 An algorithm for the numerical solution of linear differential games. Zbl 1128.91305 Polovinkin, E. S.; Ivanov, G. E.; Balashov, M. V.; Konstantinov, R. V.; Khorev, A. V. 16 2001 Uniform convexity and the splitting problem for selections. Zbl 1180.54041 Balashov, Maxim V.; Repovš, Dušan 16 2009 About the Lipschitz property of the metric projection in the Hilbert space. Zbl 1253.46075 Balashov, Maxim V.; Golubev, Maxim O. 13 2012 Maximization of a function with Lipschitz continuous gradient. Zbl 1369.90165 Balashov, M. V. 11 2015 On farthest points of sets. Zbl 1124.46007 Balashov, M. V.; Ivanov, G. E. 11 2006 Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order. Zbl 1220.46010 Balashov, Maxim V.; Repovš, Dušan 8 2011 Properties of the metric projection on weakly Vial-convex sets and parametrization of set-valued mappings with weakly convex images. Zbl 1117.52001 Balashov, M. V.; Ivanov, G. E. 8 2006 Antidistance and antiprojection in the Hilbert space. Zbl 1334.49046 Balashov, M. V. 7 2015 The gradient projection algorithm for a proximally smooth set and a function with Lipschitz continuous gradient. Zbl 1447.90036 Balashov, Maxim V. 6 2020 On polyhedral approximations in an \(n\)-dimensional space. Zbl 1356.41008 Balashov, M. V. 5 2016 On the \(P\)-property of convex compact sets. Zbl 1052.52004 Balashov, M. V. 5 2002 Weakly convex sets and modulus of nonconvexity. Zbl 1206.52004 Balashov, Maxim V.; Repovš, Dušan 5 2010 Error bound conditions and convergence of optimization methods on smooth and proximally smooth manifolds. Zbl 1490.90224 Balashov, M. V.; Tremba, A. A. 5 2022 The gradient projection algorithm for smooth sets and functions in nonconvex case. Zbl 1473.90124 Balashov, Maxim V. 5 2021 Gradient projection method on matrix manifolds. Zbl 1452.90248 Balashov, M. V. 5 2020 The farthest and the nearest points of sets. Zbl 1411.41021 Balashov, Maxim V.; Ivanov, Grigorii E. 5 2018 On Pliś metric on the space of strictly convex compacta. Zbl 1251.54005 Balashov, Maxim Viktorovich; Repovs, Dusan 4 2012 Sufficient conditions for the linear convergence of an algorithm for finding the metric projection of a point onto a convex compact set. Zbl 1527.90154 Balashov, M. V. 4 2023 On the splitting problem for selections. Zbl 1169.54007 Balashov, Maxim V.; Repovš, Dušan 4 2009 Polyhedral approximations of strictly convex compacta. Zbl 1226.52001 Balashov, Maxim V.; Repovš, Dušan 4 2011 Weak convexity of the distance function. Zbl 1276.46061 Balashov, Maxim V. 4 2013 On the gradient projection method for weakly convex functions on a proximally smooth set. Zbl 1456.90155 Balashov, M. V. 4 2020 An analogue of the Kreĭn-Milman theorem for a strongly convex hull in a Hilbert space. Zbl 1028.46026 Balashov, M. V. 3 2002 The strong convexity supporting condition and the Lipschitz condition for the metric projection. Zbl 1545.90131 Balashov, M. V.; Biglov, K. Z. 3 2024 Strong convexity of reachable sets of linear systems. Zbl 1520.93034 Balashov, Maxim V. 3 2022 The gradient projection method with Armijo’s step size on manifolds. Zbl 1481.65087 Balashov, M. V.; Kamalov, R. A. 3 2021 The Pliś metric and Lipschitz stability of minimization problems. Zbl 1423.49023 Balashov, Maksim Viktorovich 3 2019 On the geometric difference of multivalued mappings. Zbl 1037.47034 Balashov, M. V. 2 2001 Lipschitz continuous parametrizations of set-valued maps with weakly convex images. Zbl 1143.52003 Ivanov, G. E.; Balashov, M. V. 2 2007 Approximate calculation of the Chebyshev center for a convex compact set in \(\mathbb{R}^n\). Zbl 1486.52005 Balashov, Maxim V. 2 2022 Covering a set by a convex compactum: error estimates and computation. Zbl 1505.90141 Balashov, M. V. 2 2022 Stability of minimization problems and the error bound condition. Zbl 07563240 Balashov, Maxim V. 2 2022 Proximal smoothness of a set with the Lipschitz metric projection. Zbl 1315.46016 Balashov, Maxim V. 1 2013 Weak concavity of the antidistance function. Zbl 1311.49034 Balashov, Maxim V.; Golubev, Maxim O. 1 2014 Intersection of a set with a hyperplane. Zbl 1342.49022 Balashov, Maxim V. 1 2016 Lipschitz stability of extremal problems with a strongly convex set. Zbl 1440.46020 Balashov, Maxim V. 1 2020 Optimization of the reachable set of a linear system with respect to another set. Zbl 1527.49017 Balashov, M. V.; Kamalov, R. A. 1 2023 Properties of \(P\) -sets and trapped compact convex sets. Zbl 1155.52301 Balashov, M. V.; Bogdanov, I. I. 1 2008 The Lipschitz property of the metric projection in the Hilbert space. Zbl 07255592 Balashov, M. V. 1 2020 Embedding of a homothete in a convex compactum: an algorithm and its convergence. Zbl 1513.90136 Balashov, Maksim Viktorovich 1 2022 The strong convexity supporting condition and the Lipschitz condition for the metric projection. Zbl 1545.90131 Balashov, M. V.; Biglov, K. Z. 3 2024 Sufficient conditions for the linear convergence of an algorithm for finding the metric projection of a point onto a convex compact set. Zbl 1527.90154 Balashov, M. V. 4 2023 Optimization of the reachable set of a linear system with respect to another set. Zbl 1527.49017 Balashov, M. V.; Kamalov, R. A. 1 2023 Error bound conditions and convergence of optimization methods on smooth and proximally smooth manifolds. Zbl 1490.90224 Balashov, M. V.; Tremba, A. A. 5 2022 Strong convexity of reachable sets of linear systems. Zbl 1520.93034 Balashov, Maxim V. 3 2022 Approximate calculation of the Chebyshev center for a convex compact set in \(\mathbb{R}^n\). Zbl 1486.52005 Balashov, Maxim V. 2 2022 Covering a set by a convex compactum: error estimates and computation. Zbl 1505.90141 Balashov, M. V. 2 2022 Stability of minimization problems and the error bound condition. Zbl 07563240 Balashov, Maxim V. 2 2022 Embedding of a homothete in a convex compactum: an algorithm and its convergence. Zbl 1513.90136 Balashov, Maksim Viktorovich 1 2022 The gradient projection algorithm for smooth sets and functions in nonconvex case. Zbl 1473.90124 Balashov, Maxim V. 5 2021 The gradient projection method with Armijo’s step size on manifolds. Zbl 1481.65087 Balashov, M. V.; Kamalov, R. A. 3 2021 Gradient projection and conditional gradient methods for constrained nonconvex minimization. Zbl 1437.49024 Balashov, M. V.; Polyak, B. T.; Tremba, A. A. 23 2020 The gradient projection algorithm for a proximally smooth set and a function with Lipschitz continuous gradient. Zbl 1447.90036 Balashov, Maxim V. 6 2020 Gradient projection method on matrix manifolds. Zbl 1452.90248 Balashov, M. V. 5 2020 On the gradient projection method for weakly convex functions on a proximally smooth set. Zbl 1456.90155 Balashov, M. V. 4 2020 Lipschitz stability of extremal problems with a strongly convex set. Zbl 1440.46020 Balashov, Maxim V. 1 2020 The Lipschitz property of the metric projection in the Hilbert space. Zbl 07255592 Balashov, M. V. 1 2020 The Pliś metric and Lipschitz stability of minimization problems. Zbl 1423.49023 Balashov, Maksim Viktorovich 3 2019 The farthest and the nearest points of sets. Zbl 1411.41021 Balashov, Maxim V.; Ivanov, Grigorii E. 5 2018 About the gradient projection algorithm for a strongly convex function and a proximally smooth set. Zbl 1375.46056 Balashov, Maxim V. 16 2017 On polyhedral approximations in an \(n\)-dimensional space. Zbl 1356.41008 Balashov, M. V. 5 2016 Intersection of a set with a hyperplane. Zbl 1342.49022 Balashov, Maxim V. 1 2016 Maximization of a function with Lipschitz continuous gradient. Zbl 1369.90165 Balashov, M. V. 11 2015 Antidistance and antiprojection in the Hilbert space. Zbl 1334.49046 Balashov, M. V. 7 2015 Weak concavity of the antidistance function. Zbl 1311.49034 Balashov, Maxim V.; Golubev, Maxim O. 1 2014 Weak convexity of the distance function. Zbl 1276.46061 Balashov, Maxim V. 4 2013 Proximal smoothness of a set with the Lipschitz metric projection. Zbl 1315.46016 Balashov, Maxim V. 1 2013 About the Lipschitz property of the metric projection in the Hilbert space. Zbl 1253.46075 Balashov, Maxim V.; Golubev, Maxim O. 13 2012 On Pliś metric on the space of strictly convex compacta. Zbl 1251.54005 Balashov, Maxim Viktorovich; Repovs, Dusan 4 2012 Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order. Zbl 1220.46010 Balashov, Maxim V.; Repovš, Dušan 8 2011 Polyhedral approximations of strictly convex compacta. Zbl 1226.52001 Balashov, Maxim V.; Repovš, Dušan 4 2011 Weakly convex sets and modulus of nonconvexity. Zbl 1206.52004 Balashov, Maxim V.; Repovš, Dušan 5 2010 Weakly convex and proximally smooth sets in Banach spaces. Zbl 1179.46013 Balashov, M. V.; Ivanov, G. E. 31 2009 Uniform convexity and the splitting problem for selections. Zbl 1180.54041 Balashov, Maxim V.; Repovš, Dušan 16 2009 On the splitting problem for selections. Zbl 1169.54007 Balashov, Maxim V.; Repovš, Dušan 4 2009 Properties of \(P\) -sets and trapped compact convex sets. Zbl 1155.52301 Balashov, M. V.; Bogdanov, I. I. 1 2008 Elements of convex and strongly convex analysis. 2nd ed. (Элементы выпуклого и силпно выпуклого анализа.) Zbl 1181.26028 Polovinkin, E. S.; Balashov, M. V. 81 2007 Lipschitz continuous parametrizations of set-valued maps with weakly convex images. Zbl 1143.52003 Ivanov, G. E.; Balashov, M. V. 2 2007 On farthest points of sets. Zbl 1124.46007 Balashov, M. V.; Ivanov, G. E. 11 2006 Properties of the metric projection on weakly Vial-convex sets and parametrization of set-valued mappings with weakly convex images. Zbl 1117.52001 Balashov, M. V.; Ivanov, G. E. 8 2006 On the \(P\)-property of convex compact sets. Zbl 1052.52004 Balashov, M. V. 5 2002 An analogue of the Kreĭn-Milman theorem for a strongly convex hull in a Hilbert space. Zbl 1028.46026 Balashov, M. V. 3 2002 An algorithm for the numerical solution of linear differential games. Zbl 1128.91305 Polovinkin, E. S.; Ivanov, G. E.; Balashov, M. V.; Konstantinov, R. V.; Khorev, A. V. 16 2001 On the geometric difference of multivalued mappings. Zbl 1037.47034 Balashov, M. V. 2 2001 \(M\)-strongly convex subsets and their generating sets. Zbl 1004.46014 Balashov, M. V.; Polovinkin, E. S. 42 2000 all cited Publications top 5 cited Publications all top 5 Cited by 182 Authors 40 Balashov, Maxim Viktorovich 12 Ivanov, Grigorii E. 11 Dudov, Sergeĭ Ivanovich 9 Alimov, Alexey R. 9 Polovinkin, Evgenii Sergeevich 8 Osiptsev, Mikhaĭl Anatol’evich 7 Thibault, Lionel 7 Ushakov, Vladimir Nikolaevich 6 Ershov, Aleksandr Anatol’evich 5 Lopushanski, Mariana S. 5 Patsko, Valerii S. 5 Repovš, Dušan D. 5 Tsar’kov, Igor’ Germanovich 4 Kumkov, Sergey S. 4 Kurzhanskiĭ, Aleksandr Borisovich 4 Nacry, Florent 4 Orlov, Igor Vladimirovich 4 Tremba, Andrey Aleksandrovich 3 Biglov, Kamil Z. 3 Ibragimov, Danis N. 3 Lukoyanov, Nikolaĭ Yur’evich 3 Plotnikov, Andreĭ Viktorovich 3 Sirotin, A. N. 2 Abramova, Veronika Valer’evna 2 Adly, Samir 2 Bui, Vuong 2 Daryin, Alexander N. 2 De Bernardi, Carlo Alberto 2 Dolgopolik, Maxim Vladimirovich 2 Flerov, A. A. 2 Galkin, Oleg Evgen’evich 2 Galkina, Svetlana Yur’evna 2 Gomoyunov, Mikhail Igorevich 2 Ivanov, Grigory M. 2 Kamalov, Rinat A. 2 Karasev, Roman N. 2 Khachatryan, Rafik Agasievich 2 Komleva, Tatyana A. 2 Konstantinov, Matey 2 Kornev, Dmitriĭ Vasil’evich 2 Martini, Horst 2 Matviĭchuk, Aleksandr Rostislavovich 2 Meshcheryakova, E. A. 2 Nikol’skiĭ, Mikhaĭl Sergeevich 2 Polyak, Boris Teodorovich 2 Rinaldi, Francesco 2 Sakbaev, Vsevolod Zhanovich 2 Semenov, Pavel Vladimirovič 2 Shirokov, Maksim Evgen’evich 2 Skripnik, Natalia Viktorovna 2 Taras’ev, Aleksandr Mikhaĭlovich 2 Ushakov, Andreĭ Vladimirovich 2 Veselý, Libor 2 Vuong, Phan Tu 2 Zeffiro, Damiano 2 Zlateva, Nadia P. 1 Ansary Karbasy, Saeid 1 Anwary, Mohammad Kazem 1 Arkhipov, P. A. 1 Arutyunov, Aram Vladimirovic 1 Avkhadiev, Farit Gabidinovich 1 Babenko, Viktor V. 1 Babenko, Vladyslav Fedorovych 1 Baran, I. V. 1 Basit, Bushra 1 Bednov, Borislav Borisovich 1 Bogdanov, Ilya I. 1 Bomze, Immanuel M. 1 Cabot, A. 1 Castaing, Charles 1 Chang, Huibin 1 Chen, Xuesong 1 Chorianopoulos, Christos 1 Davis, Damek Shea 1 Drusvyatskiy, Dmitriy 1 Druzhinin, Yu. Yu. 1 Efremov, Roman V. 1 Fatkhullin, I. F. 1 Ferreira, Orizon Pereira 1 Ganebny, Sergei A. 1 Gao, Yingchao 1 Gerstner, Philipp 1 Golubev, Maxim O. 1 Gorokhovik, Valentin Vikent’evich 1 Graf, Sergey Yu. 1 Grzybowski, Jerzy 1 Gudovich, Anastasia Nikolaevna 1 He, Chan 1 Heuveline, Vincent 1 Holmsen, Andreas F. 1 Iranmanesh, Mahdi 1 Ivanov, Illya 1 Ivan’shin, Pëtr Nikolaevich 1 Izmest’ev, Igor’ Vyacheslavovich 1 Jahn, Thomas 1 Jourani, Abderrahim 1 Kamenskiĭ, Mikhaĭl Igor’evich 1 Khabibullin, Bulat Nurmievich 1 Khademzadeh, Hamid Reza 1 Khalilova, Zarema I. ...and 82 more Authors all top 5 Cited in 73 Serials 19 Mathematical Notes 17 Journal of Mathematical Sciences (New York) 15 Journal of Convex Analysis 13 Computational Mathematics and Mathematical Physics 13 Proceedings of the Steklov Institute of Mathematics 8 Journal of Mathematical Analysis and Applications 8 Sbornik: Mathematics 5 Automation and Remote Control 5 Russian Mathematics 5 Differential Equations 5 Set-Valued and Variational Analysis 3 Ukrainian Mathematical Journal 3 Topology and its Applications 3 Discrete & Computational Geometry 3 Journal of Global Optimization 3 SIAM Journal on Optimization 3 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 3 Izvestiya Instituta Matematiki i Informatiki. Udmurtskiĭ Gosudarstvennyĭ Universitet 2 Russian Mathematical Surveys 2 Applied Mathematics and Optimization 2 Proceedings of the American Mathematical Society 2 Optimization 2 Computational Mathematics and Modeling 2 Mathematical Programming. Series A. Series B 2 Cybernetics and Systems Analysis 2 Topological Methods in Nonlinear Analysis 2 Doklady Mathematics 2 Asian-European Journal of Mathematics 2 Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki 2 Vestnik Rossiĭskikh Universitetov. Matematika 1 Computers & Mathematics with Applications 1 Discrete Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Computational Physics 1 Linear and Multilinear Algebra 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Prikladnaya Matematika i Mekhanika 1 Theory of Probability and its Applications 1 Advances in Mathematics 1 Archiv der Mathematik 1 Journal of Approximation Theory 1 Journal of Geometry 1 Journal of Optimization Theory and Applications 1 Mathematika 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Pacific Journal of Mathematics 1 Siberian Mathematical Journal 1 Transactions of the Moscow Mathematical Society 1 Moscow University Computational Mathematics and Cybernetics 1 Journal of Scientific Computing 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Vestnik St. Petersburg University. Mathematics 1 Computational Optimization and Applications 1 Journal of Computer and Systems Sciences International 1 Russian Journal of Mathematical Physics 1 Journal of Applied Analysis 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 Abstract and Applied Analysis 1 International Game Theory Review 1 Doklady Natsional’noĭ Akademii Nauk Belarusi 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Journal of Fixed Point Theory and Applications 1 Optimization Letters 1 European Journal of Pure and Applied Mathematics 1 International Electronic Journal of Geometry 1 Banach Journal of Mathematical Analysis 1 Matematicheskaya Teoriya Igr i eë Prilozheniya 1 Dynamic Games and Applications 1 Problemy Analiza. Issues of Analysis all top 5 Cited in 37 Fields 60 Calculus of variations and optimal control; optimization (49-XX) 52 Convex and discrete geometry (52-XX) 48 Functional analysis (46-XX) 45 Operations research, mathematical programming (90-XX) 32 Approximations and expansions (41-XX) 21 Systems theory; control (93-XX) 18 Operator theory (47-XX) 16 Numerical analysis (65-XX) 15 Real functions (26-XX) 14 Ordinary differential equations (34-XX) 13 General topology (54-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Probability theory and stochastic processes (60-XX) 3 Functions of a complex variable (30-XX) 3 Partial differential equations (35-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Computer science (68-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) Citations by Year