Edit Profile (opens in new tab) Arutyunov, Aram Vladimirovic Co-Author Distance Author ID: arutyunov.aram-v Published as: Arutyunov, A. V.; Arutyunov, Aram V.; Arutyunov, Aram; Arutyunov, Aram Vladimirovich; Arutyunov, A.; Arutjunov, A. V. more...less Further Spellings: Арутюнов Арам Владимирович Homepage: http://sa.cs.msu.su/staff/arutyunov External Links: ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND Documents Indexed: 251 Publications since 1978, including 4 Books Biographic References: 1 Publication Co-Authors: 99 Co-Authors with 157 Joint Publications 3,010 Co-Co-Authors all top 5 Co-Authors 78 single-authored 30 Karamzin, Dmitry Yu. 24 Zhukovskiĭ, Sergeĭ Evgen’evich 21 Izmailov, Alekseĭ F. 20 Lobo Pereira, Fernando 17 Avakov, Evgeniĭ Rachievich 16 Zhukovskiĭ, Evgeniĭ Semenovich 11 Tynyanskij, N. T. 5 Gel’man, Boris Danielovich 5 Pavlova, Natalia G. 4 Aseev, Sergei M. 4 Chernikova, Natalia Yu. 4 Greshnov, Aleksandr Valer’evich 4 Jaćimović, Vladimir 3 Blagodatskikh, Viktor Ivanovich 3 Il’in, Vladimir Aleksandrovich 3 Korovin, Sergeĭ Konstantinovich 3 Obukhovskiĭ, Valeriĭ Vladimirovich 3 Osipenko, Konstantin Yur’evich 3 Zhukovskaya, Zukhra Tagurovna 2 Agrachev, Andreĭ Aleksandrovich 2 Bogovskij, M. E. 2 Buslaev, Aleksandr Pavlovich 2 Demidovich, Vasiliĭ Borisovich 2 Dezin, Alekseĭ Alekseevich 2 Emel’yanov, Stanislav Vasil’evich 2 Galeev, Eh. M. 2 Gol’dman, Mikhail L’vovich 2 Kusraev, Anatoly Georgievich 2 Kutateladze, Semën Samsonovich 2 Mardanov, Misir Dzhumail ogly 2 Marinković, Boban 2 Maslov, Viktor Pavlovich 2 Mishchenko, Evgeniĭ Frolovich 2 Mordukhovich, Boris S. 2 Pluzhnikova, Elena Aleksandrovna 2 Samoĭlenko, Anatoliĭ Mykhaĭlovych 2 Shananin, Aleksandr Alekseevich 2 Shemyakina, Tamara Kuz’minichna 2 Shvartsman, Ilya A. 2 Storozhuk, Konstantin Valer’evich 2 Tikhomirov, Vladimir Mikhaĭlovich 2 Vinter, Richard B. 2 Zerkalov, Leonid G. 1 Bakhvalov, Nikolaĭ Sergeevich 1 Ber, G. Z. 1 Bibikov, Yuriĭ Nikolaevich 1 Bobylev, Nikolaĭ Antonovich 1 Borukhov, Valentin Terent’evich 1 Borzova, M. V. 1 Burkov, Vladimir N. 1 Burlakov, Evgenii O. 1 Chentsov, Aleksandr Georgievich 1 de Oliveira, Valeriano Antunes 1 Dmitruk, Andrei V. 1 Filippov, Vladimir Mikhaĭlovich 1 Filippova, Ol’ga Viktorovna 1 Fomicheva, Yu. G. 1 Gaĭshun, Ivan Vasil’evich 1 Gorbunova, S. V. 1 Grigorenko, Anna A. 1 Izobov, Nikolaĭ Alekseevich 1 Kiguradze, Ivan Tarielovich 1 Korzyuk, Viktor Ivanovich 1 Kostyukova, Olga Ivanova 1 Kruglova, E. V. 1 Kudryavtsev, Lev Dmitrievich 1 Kurzhanskiĭ, Aleksandr Borisovich 1 Lavrent’ev, Mikhail Mikhaĭlovich 1 Lokutsievskiy, Lev Viacheslavovich 1 Magaril-Il’yaev, Gregoriĭ Geogrievich 1 Makarov, Evgeniĭ Konstantinovich 1 Maksimov, Vladimir Petrovich 1 Marinkovich, B. 1 Martynyuk, Anatoliĭ Andriĭovych 1 Mazanik, Sergeĭ Alekseevich 1 Mingaleeva, Z. T. 1 Moiseev, Evgeniĭ Ivanovich 1 Nikol’skii, A. M. 1 Okoulevitch, A. I. 1 Osipov, Yuriĭ Sergeevich 1 Panasenko, Elena Aleksandrovna 1 Pliss, Viktor Aleksandrovich 1 Polovinkin, Evgenii Sergeevich 1 Ponosov, Arkadiĭ Vladimirovich 1 Rozov, Nikolaĭ Khristovich 1 Rozova, V. N. 1 Sadovnichiĭ, Viktor Antonovich 1 Salikhova, K. I. 1 Shindyapin, Andreĭ Igorevich 1 Silva, Geraldo Nunes 1 Uspenskiĭ, Stanislav Viktorovich 1 Vartapetov, S. A. 1 Vasil’ev, Fedor Pavlovich 1 Vereshchagina, Yu. S. 1 Vladimirov, Vasiliĭ Sergeevich 1 Yurchuk, Nikolay Iossifovich 1 Zalozhnev, A. Yu. 1 Zerkalov, N. V. 1 Zhukovskiy, Sergey Evgenyevich all top 5 Serials 28 Doklady Mathematics 28 Differential Equations 12 Mathematical Notes 12 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 11 Journal of Optimization Theory and Applications 10 Proceedings of the Steklov Institute of Mathematics 8 Sbornik: Mathematics 7 Moscow University Computational Mathematics and Cybernetics 6 Soviet Mathematics. Doklady 5 Russian Mathematical Surveys 5 SIAM Journal on Optimization 5 Journal of Mathematical Sciences (New York) 5 Set-Valued and Variational Analysis 4 Differential Equations 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 SIAM Journal on Control and Optimization 4 Topology and its Applications 4 Izvestiya: Mathematics 4 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 3 Journal of Mathematical Analysis and Applications 3 Mathematics of Operations Research 3 Siberian Mathematical Journal 3 Vestnik Moskovskogo Universiteta. Seriya 15 3 Mathematical Programming. Series A. Series B 3 Russian Academy of Sciences. Doklady. Mathematics 3 Vestnik Rossiĭskikh Universitetov. Matematika 2 Applicable Analysis 2 Differentsial’nye Uravneniya 2 Functional Analysis and its Applications 2 Soobshcheniya Akademii Nauk Gruzinskoĭ SSR 2 Systems & Control Letters 2 Optimization 2 Soviet Journal of Computer and Systems Sciences 2 Computational Mathematics and Mathematical Physics 2 Vestnik Rossiĭskogo Universiteta Druzhby Narodov. Seriya Matematika 2 Journal of Dynamical and Control Systems 2 Journal of Fixed Point Theory and Applications 2 Eurasian Mathematical Journal 1 Computers & Mathematics with Applications 1 Matematicheskie Zametki 1 Moscow University Mathematics Bulletin 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Journal of Soviet Mathematics 1 Mathematics of the USSR. Izvestiya 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Transactions of the American Mathematical Society 1 Journal of Global Optimization 1 YUJOR. Yugoslav Journal of Operations Research 1 Automation and Remote Control 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Mathematics of the USSR, Sbornik 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Matematicheskiĭ Sbornik 1 Set-Valued Analysis 1 Russian Academy of Sciences. Izvestiya. Mathematics 1 Russian Academy of Sciences. Sbornik. Mathematics 1 Journal of Convex Analysis 1 Discrete and Continuous Dynamical Systems 1 Matematicheskoe Modelirovanie 1 Trudy Instituta Prikladnoĭ Matematiki Imeni I. N. Vekua 1 Fixed Point Theory 1 Lecture Notes in Control and Information Sciences 1 Mathematics and its Applications (Dordrecht) 1 Vychislitel’nye Metody i Programmirovanie 1 Optimization Letters 1 Nonlinear Analysis. Theory, Methods & Applications 1 De Gruyter Graduate all top 5 Fields 146 Calculus of variations and optimal control; optimization (49-XX) 49 Operator theory (47-XX) 47 Operations research, mathematical programming (90-XX) 38 General topology (54-XX) 28 Systems theory; control (93-XX) 24 Ordinary differential equations (34-XX) 17 Global analysis, analysis on manifolds (58-XX) 15 Functional analysis (46-XX) 13 Real functions (26-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 History and biography (01-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Numerical analysis (65-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Approximations and expansions (41-XX) 2 Convex and discrete geometry (52-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 179 Publications have been cited 1,427 times in 554 Documents Cited by ▼ Year ▼ Covering mappings in metric spaces and fixed points. Zbl 1152.54351Arutyunov, A. V. 79 2007 Locally covering maps in metric spaces and coincidence points. Zbl 1182.54050Arutyunov, Aram; Avakov, Evgeniy; Gel’man, Boris; Dmitruk, Andrei; Obukhovskii, Valeri 49 2009 Optimality conditions. Abnormal and degenerate problems. Translated from the Russian by S. A. Vakhrameev. Zbl 0987.49001Arutyunov, Aram V. 47 2000 Stability of coincidence points and properties of covering mappings. Zbl 1186.54033Arutyunov, A. V. 41 2009 Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints. Zbl 0873.49014Arutyunov, Aram V.; Aseev, Sergei M. 41 1997 The maximum principle for optimal control problems with state constraints by R.V. Gamkrelidze: Revisited. Zbl 1221.49026Arutyunov, A. V.; Karamzin, D. Y.; Pereira, F. L. 34 2011 Covering mappings and their applications to differential equations unsolved for the derivative. Zbl 1204.54015Avakov, E. R.; Arutyunov, A. V.; Zhukovskii, E. S. 34 2009 Extremum conditions. Abnormal and degenerate problems. (Usloviya ehkstremuma. Anormal’nye i vyrozhdennye zadachi.) Zbl 0953.49001Arutyunov, A. V. 31 1997 A nondegenerate maximum principle for the impulse control problem with state constraints. Zbl 1116.49013Arutyunov, A.; Karamzin, D.; Pereira, F. 29 2005 Covering mappings and well-posedness of nonlinear Volterra equations. Zbl 1237.45003Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 26 2012 Coincidence points principle for mappings in partially ordered spaces. Zbl 1305.54048Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 25 2015 On the well-posedness of differential equations unsolved for the derivative. Zbl 1252.34009Arutyunov, A. V.; Zhukovskii, E. S.; Zhukovskii, S. E. 24 2011 Theory of \((q_1,q_2)\)-quasimetric spaces and coincidence points. Zbl 1352.54030Arutyunov, A. V.; Greshnov, A. V. 24 2016 Perturbations of extremal problems with constraints and necessary optimality conditions. Zbl 0726.49015Arutyunov, A. V. 24 1991 Second-order conditions in extremal problems. The abnormal points. Zbl 0922.49017Arutyunov, A. V. 24 1998 A simple ‘finite approximations’ proof of the Pontryagin maximum principle under reduced differentiability hypotheses. Zbl 1046.49014Arutyunov, Aram V.; Vinter, Richard B. 24 2004 Stability theorems for estimating the distance to a set of coincidence points. Zbl 1326.54042Arutyunov, A. V.; Avakov, E. R.; Zhukovskiy, S. E. 20 2015 \((q_1,q_2)\)-quasimetric spaces. Covering mappings and coincidence points. Zbl 1401.54023Arutyunov, Aram V.; Greshnov, Alexandr V. 19 2018 Directional regularity and metric regularity. Zbl 1262.49026Arutyunov, Aram V.; Avakov, Evgeniy R.; Izmailov, Alexey F. 19 2007 Smooth abnormal problems in extremum theory and analysis. Zbl 1367.47065Arutyunov, A. V. 19 2012 Topological and geometrical properties of spaces with symmetric and nonsymmetric \(f\)-quasimetrics. Zbl 1377.54028Arutyunov, A. V.; Greshnov, A. V.; Lokutsievskii, L. V.; Storozhuk, K. V. 19 2017 On constrained impulsive control problems. Zbl 1288.49013Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L. 18 2010 Directional stability theorem and directional metric regularity. Zbl 1262.49027Arutyunov, Aram V.; Izmailov, Alexey F. 18 2006 Coincidence points principle for set-valued mappings in partially ordered spaces. Zbl 1335.54041Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 18 2016 First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints. Zbl 0834.49013Arutyunov, A. V.; Aseev, S. M.; Blagodatskikh, V. I. 15 1993 On coincidence points of mappings in partially ordered spaces. Zbl 1312.54018Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 15 2013 Coincidence points of set-valued mappings in partially ordered spaces. Zbl 1301.49041Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 15 2013 State constraints in optimal control. The degeneracy phenomenon. Zbl 0873.49015Arutyunov, A. V.; Aseev, S. M. 15 1995 Necessary optimality conditions for discrete optimal control problems. Zbl 1109.49022Arutyunov, A. V.; Marinkovich, B. 15 2005 Abnormal extremal problems and optimality conditions. Zbl 0894.90133Arutyunov, A. V. 15 1997 On a generalization of the impulsive control concept: controlling system jumps. Zbl 1209.49048Arutyunov, Aram; Karamzin, Dmitry; Pereira, Fernando L. 15 2011 Pontryagin’s maximum principle for constrained impulsive control problems. Zbl 1236.49046Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. 15 2012 Necessary conditions for an extremum in a mathematical programming problem. Zbl 1160.49016Avakov, E. R.; Arutyunov, A. V.; Izmailov, A. F. 14 2007 Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points. Zbl 1336.49005Arutyunov, A. V. 14 2015 Non-degenerate necessary optimality conditions for the optimal control problem with equality-type state constraints. Zbl 1339.49019Arutyunov, A. V.; Karamzin, D. Yu. 14 2016 Existence and properties of inverse mappings. Zbl 1302.46010Arutyunov, A. V.; Zhukovskiy, S. E. 13 2010 Implicit function theorem without a priori assumptions about normality. Zbl 1210.47083Arutyunov, A. V. 13 2006 Convex and set-valued analysis. Selected topics. Zbl 1357.49001Arutyunov, Aram V.; Obukhovskii, Valeri 12 2017 Second order necessary conditions for optimal impulsive control problems. Zbl 1032.49040Arutyunov, A.; Jaćimović, V.; Pereira, F. 12 2003 Necessary conditions for impulsive nonlinear optimal control problems without a priori normality assumptions. Zbl 1104.49030Arutyunov, A.; Dykhta, V.; Lobo Pereira, F. 12 2005 Regular zeros of quadratic maps and their application. Zbl 1232.26010Arutyunov, A. V.; Karamzin, D. Yu 11 2011 A survey on regularity conditions for state-constrained optimal control problems and the non-degenerate maximum principle. Zbl 1435.49006Arutyunov, Aram; Karamzin, Dmitry 11 2020 Existence of local solutions in constrained dynamic systems. Zbl 1232.93037Arutyunov, A. V.; Zhukovskiy, S. E. 10 2011 Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications. Zbl 1149.90140Arutyunov, A. V.; Avakov, E. R.; Izmailov, A. F. 10 2008 Local solvability of control systems with mixed constraints. Zbl 1210.93026Arutyunov, A. V.; Zhukovskiy, S. E. 10 2010 On some continuity properties of the measure Lagrange multiplier from the maximum principle for state constrained problems. Zbl 1342.49057Arutyunov, A. V.; Karamzin, D. Yu. 10 2015 On the theory of the maximum principle in optimal control problems with phase constraints. Zbl 0684.34073Arutyunov, A. V. 9 1989 On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces. Zbl 1408.54014Arutyunov, Aram V.; Zhukovskiy, Evgeny S.; Zhukovskiy, Sergey E. 9 2018 Variational principles in nonlinear analysis and their generalization. Zbl 1432.49019Arutyunov, A. V.; Zhukovskiy, S. E. 9 2018 On the solvability of implicit differential inclusions. Zbl 1309.47069Arutyunov, Aram; de Oliveira, Valeriano Antunes; Lobo Pereira, Fernando; Zhukovskiy, Evgeniy; Zhukovskiy, Sergey 8 2015 Application of methods of ordinary differential equations to global inverse function theorems. Zbl 07082880Arutyunov, A. V.; Zhukovskiy, S. E. 8 2019 On necessary optimality conditions in a problem with phase constraints. Zbl 0597.49018Arutyunov, A. V. 8 1985 Coincidence points of two maps. Zbl 1304.54070Arutyunov, A. V. 8 2014 Maximum principle in problems with mixed constraints under weak assumptions of regularity. Zbl 1221.49027Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L. 8 2010 The maximum principle in optimal control problems with phase constraints. Nondegeneracy and stability. Zbl 0839.49014Arutyunov, A. V.; Aseev, S. M. 8 1994 Implicit function theorem as a realization of the Lagrange principle. Abnormal points. Zbl 0958.47036Arutyunov, A. V. 8 2000 Caristi-like condition. Existence of solutions to equations and minima of functions in metric spaces. Zbl 1454.54027Arutyunov, A. V.; Gel’man, B. D.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 7 2019 Hadamard’s theorem for mappings with relaxed smoothness conditions. Zbl 1417.54021Arutyunov, A. V.; Zhukovskiy, S. E. 7 2019 Continuous selections of solutions for locally Lipschitzian equations. Zbl 1481.47072Arutyunov, Aram V.; Izmailov, Alexey F.; Zhukovskiy, Sergey E. 7 2020 The coincidence point problem for set-valued mappings and Ulam-Hyers stability. Zbl 1419.54046Arutyunov, A. V. 7 2014 First order necessary conditions in optimal control problems with phase restrictions. Zbl 0733.49023Arutyunov, A. V. 7 1988 Second-order necessary optimality conditions for problems without a priori normality assumptions. Zbl 1278.90430Arutyunov, Aram; Lobo Pereira, Fernando 7 2006 Covering of nonlinear maps on a cone in neighborhoods of irregular points. Zbl 1096.46049Arutyunov, A. V. 7 2005 On the structure of the set of coincidence points. Zbl 1322.54026Arutyunov, A. V.; Gel’man, B. D. 7 2015 Coincidence points of multivalued mappings in \((q_1,q_2)\)-quasimetric spaces. Zbl 1410.54045Arutyunov, A. V.; Greshnov, A. V. 7 2017 Abnormal equality-constrained optimization problems: sensitivity theory. Zbl 1136.90035Arutyunov, A. V.; Izmailov, A. F. 7 2004 Coincidence points of mappings in vector metric spaces with applications to differential equations and control systems. Zbl 1384.49006Arutyunov, A. V.; Zhukovskiy, S. E. 6 2017 Variational principles in analysis and existence of minimizers for functions on metric spaces. Zbl 1451.58007Arutyunov, Aram V.; Zhukovskiy, Sergey E. 6 2019 Theorems of the alternative for systems of convex inequalities. Zbl 07058435Arutyunov, Aram V.; Zhukovskiy, Sergey E.; Marinkovic, Boban 6 2019 On the stability of fixed points and coincidence points of mappings in the generalized Kantorovich’s theorem. Zbl 1473.54046Arutyunov, Aram V.; Zhukovskiy, Evgeniy S.; Zhukovskiy, Sergey E. 6 2020 Kantorovich’s fixed point theorem in metric spaces and coincidence points. Zbl 1439.54025Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 6 2019 Two problems of the theory of quadratic maps. Zbl 1275.15015Arutyunov, A. V. 6 2012 Caristi-like condition and the existence of minima of mappings in partially ordered spaces. Zbl 1466.49024Arutyunov, Aram V.; Zhukovskiy, Evgeny S.; Zhukovskiy, Sergey E. 6 2019 On necessary second-order conditions in optimal control problems. Zbl 1095.49506Arutyunov, A. V.; Vereshchagina, Yu. S. 6 2002 Properties of the Lagrange multipliers in the Pontryagin maximum principle for optimal control problems with state constraints. Zbl 1260.49026Arutyunov, A. V. 6 2012 State constraints in impulsive control problems: Gamkrelidze-like conditions of optimality. Zbl 1331.49047Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L. 6 2015 Nonnegativity of quadratic forms on intersections of quadrics and quadratic maps. Zbl 1219.90183Arutyunov, A. V. 5 2008 The maximum principle for differential inclusions with phase constraints. Zbl 0823.49015Arutyunov, A. V.; Blagodatskikh, V. I. 5 1991 Equilibrium price as a coincidence point of two mappings. Zbl 1274.91292Arutyunov, A. V.; Zhukovskij, S. E.; Pavlova, N. G. 5 2013 Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications. Zbl 1082.90110Arutyunov, Aram V.; Izmailov, Alexey F. 5 2005 Perturbation of solutions of the coincidence point problem for two mappings. Zbl 1318.54021Arutyunov, A. V.; Zhukovskiy, S. E. 5 2014 An investigation of smooth maps in a neighbourhood of an abnormal point. Zbl 1295.26014Avakov, E. R.; Arutyunov, A. V.; Karamzin, D. Yu. 5 2014 Necessary conditions for a weak minimum in an optimal control problem with mixed constraints. Zbl 1294.49010Arutyunov, A. V.; Karamzin, D. Yu. 5 2005 Pontryagin’s maximum principle for optimal impulsive control problems. Zbl 1205.49025Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. 5 2010 Necessary optimality conditions for problems with equality and inequality constraints: Abnormal case. Zbl 1190.90263Arutyunov, A. V.; Karamzin, D. Y.; Pereira, F. L. 5 2009 Stability of possibly nonisolated solutions of constrained equations, with applications to complementarity and equilibrium problems. Zbl 06913662Arutyunov, A. V.; Izmailov, A. F. 5 2018 Optimal impulsive control. The extension approach. Zbl 1423.49001Arutyunov, Aram; Karamzin, Dmitry; Lobo Pereira, Fernando 4 2019 Maximum principle and second-order conditions for minimax problems of optimal control. Zbl 0799.49022Arutyunov, A. V.; Silin, D. B.; Zerkalov, N. V. 4 1992 On necessary conditions for a local minimum in optimal control theory. Zbl 0579.49016Arutyunov, A. V.; Tynyanskij, N. T. 4 1984 New bifurcation theorems via the second-order optimality conditions. Zbl 1168.47050Arutyunov, A. V.; Izmailov, A. F.; Jaćimović, V. 4 2009 Level set for a smooth mapping in the neighborhood of a singular point and zeros of a quadratic mapping. Zbl 0762.46028Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 4 1991 Properties of surjective real quadratic maps. Zbl 1359.15017Arutyunov, Aram V.; Zhukovskiy, Sergei E. 4 2016 Properties of extremals in optimal control problems with state constraints. Zbl 1402.49016Arutyunov, A. V.; Karamzin, Dmitry Yu. 4 2016 Tangent vectors to a zero set at abnormal points. Zbl 1035.46043Arutyunov, Aram V.; Izmailov, Alexey F. 4 2004 On implicit function theorems at abnormal points. Zbl 1229.47098Arutyunov, A. V. 3 2010 Continuous dependence of coincidence points on a parameter. Zbl 1310.47082Arutyunov, Aram; Zhukovskiy, Sergey 3 2015 Convex properties of the Legendre transform. Zbl 0455.46011Arutyunov, A. V. 3 1980 The maximum principle in a problem with phase constraints. Zbl 0591.49010Arutyunov, A. V.; Tynyanskij, N. T. 3 1984 Maximum principle and second order necessary conditions for an optimal control problem with time-lag. Zbl 0594.49015Arutyunov, A. V. 3 1986 Higher-order conditions in anormal extremal problems with constraints of equality type. Zbl 0752.49011Arutyunov, A. V. 3 1990 Global and semilocal theorems on implicit and inverse functions in Banach spaces. Zbl 07498875Arutyunov, Aram V.; Zhukovskiy, Sergey E. 1 2022 Kantorovich’s fixed point theorem and coincidence point theorems for mappings in vector metric spaces. Zbl 1506.54016Arutyunov, Aram V.; Zhukovskiy, Evgeny S.; Zhukovskiy, Sergey E.; Zhukovskaya, Zukhra T. 1 2022 On global solvability of nonlinear equations with parameters. Zbl 1494.47094Arutyunov, A. V.; Zhukovskiy, S. E. 1 2021 Stable solvability of nonlinear equations under completely continuous perturbations. Zbl 07343907Arutyunov, A. V.; Zhukovskiy, S. E. 1 2021 Covering mappings acting into normed spaces and coincidence points. Zbl 1481.54032Arutyunov, A. V.; Zhukovskiy, S. E. 1 2021 Existence of real solutions of nonlinear equations without a priori normality assumptions. Zbl 1481.26010Arutyunov, A. V. 1 2021 A survey on regularity conditions for state-constrained optimal control problems and the non-degenerate maximum principle. Zbl 1435.49006Arutyunov, Aram; Karamzin, Dmitry 11 2020 Continuous selections of solutions for locally Lipschitzian equations. Zbl 1481.47072Arutyunov, Aram V.; Izmailov, Alexey F.; Zhukovskiy, Sergey E. 7 2020 On the stability of fixed points and coincidence points of mappings in the generalized Kantorovich’s theorem. Zbl 1473.54046Arutyunov, Aram V.; Zhukovskiy, Evgeniy S.; Zhukovskiy, Sergey E. 6 2020 Nonlocal generalized implicit function theorems in Hilbert spaces. Zbl 07304912Arutyunov, A. V.; Zhukovskiy, S. E. 2 2020 On stability of continuous extensions of mappings with respect to Nemytskii operator. Zbl 07424583Arutyunov, A. V.; Zhukovskiy, S. E. 1 2020 Covering on a convex set in the absence of Robinson’s regularity. Zbl 1501.47099Arutyunov, Aram V.; Izmailov, Alexey F. 1 2020 Lower bound of the upper topological limit of a sequence of subspaces. Zbl 1454.46026Arutyunov, Aram V. 1 2020 Necessary optimality conditions for optimal control problems in the presence of degeneration. Zbl 1445.49016Arutyunov, A. V.; Zhukovskiy, S. E. 1 2020 Application of methods of ordinary differential equations to global inverse function theorems. Zbl 07082880Arutyunov, A. V.; Zhukovskiy, S. E. 8 2019 Caristi-like condition. Existence of solutions to equations and minima of functions in metric spaces. Zbl 1454.54027Arutyunov, A. V.; Gel’man, B. D.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 7 2019 Hadamard’s theorem for mappings with relaxed smoothness conditions. Zbl 1417.54021Arutyunov, A. V.; Zhukovskiy, S. E. 7 2019 Variational principles in analysis and existence of minimizers for functions on metric spaces. Zbl 1451.58007Arutyunov, Aram V.; Zhukovskiy, Sergey E. 6 2019 Theorems of the alternative for systems of convex inequalities. Zbl 07058435Arutyunov, Aram V.; Zhukovskiy, Sergey E.; Marinkovic, Boban 6 2019 Kantorovich’s fixed point theorem in metric spaces and coincidence points. Zbl 1439.54025Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 6 2019 Caristi-like condition and the existence of minima of mappings in partially ordered spaces. Zbl 1466.49024Arutyunov, Aram V.; Zhukovskiy, Evgeny S.; Zhukovskiy, Sergey E. 6 2019 Optimal impulsive control. The extension approach. Zbl 1423.49001Arutyunov, Aram; Karamzin, Dmitry; Lobo Pereira, Fernando 4 2019 Investigation of the sets of real solutions of non-linear equations. Zbl 1443.26005Arutyunov, A. V. 2 2019 Generalized Weierstrass condition in the classical calculus of variations. Zbl 1421.49016Arutyunov, A. V. 2 2019 \((q_1,q_2)\)-quasimetric spaces. Covering mappings and coincidence points. Zbl 1401.54023Arutyunov, Aram V.; Greshnov, Alexandr V. 19 2018 On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces. Zbl 1408.54014Arutyunov, Aram V.; Zhukovskiy, Evgeny S.; Zhukovskiy, Sergey E. 9 2018 Variational principles in nonlinear analysis and their generalization. Zbl 1432.49019Arutyunov, A. V.; Zhukovskiy, S. E. 9 2018 Stability of possibly nonisolated solutions of constrained equations, with applications to complementarity and equilibrium problems. Zbl 06913662Arutyunov, A. V.; Izmailov, A. F. 5 2018 New conditions for the existence of equilibrium prices. Zbl 1461.91177Arutyunov, Aram V.; Pavlova, Natalia G.; Shananin, Aleksandr A. 1 2018 Second-order necessary optimality conditions in optimal impulsive control problems. Zbl 1408.49031Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L.; Chernikova, N. Yu. 1 2018 Recovering linear operators and Lagrange function minimality condition. Zbl 1396.41022Arutyunov, A. V.; Osipenko, K. Yu. 1 2018 Topological and geometrical properties of spaces with symmetric and nonsymmetric \(f\)-quasimetrics. Zbl 1377.54028Arutyunov, A. V.; Greshnov, A. V.; Lokutsievskii, L. V.; Storozhuk, K. V. 19 2017 Convex and set-valued analysis. Selected topics. Zbl 1357.49001Arutyunov, Aram V.; Obukhovskii, Valeri 12 2017 Coincidence points of multivalued mappings in \((q_1,q_2)\)-quasimetric spaces. Zbl 1410.54045Arutyunov, A. V.; Greshnov, A. V. 7 2017 Coincidence points of mappings in vector metric spaces with applications to differential equations and control systems. Zbl 1384.49006Arutyunov, A. V.; Zhukovskiy, S. E. 6 2017 Second-order optimality conditions for singular extremals in optimal control problems with equality endpoint constraints. Zbl 1373.49022Arutyunov, A. V.; Shvartsman, I. A.; Zhukovskaya, Z. T. 1 2017 Theory of \((q_1,q_2)\)-quasimetric spaces and coincidence points. Zbl 1352.54030Arutyunov, A. V.; Greshnov, A. V. 24 2016 Coincidence points principle for set-valued mappings in partially ordered spaces. Zbl 1335.54041Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 18 2016 Non-degenerate necessary optimality conditions for the optimal control problem with equality-type state constraints. Zbl 1339.49019Arutyunov, A. V.; Karamzin, D. Yu. 14 2016 Properties of surjective real quadratic maps. Zbl 1359.15017Arutyunov, Aram V.; Zhukovskiy, Sergei E. 4 2016 Properties of extremals in optimal control problems with state constraints. Zbl 1402.49016Arutyunov, A. V.; Karamzin, Dmitry Yu. 4 2016 Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints. Zbl 1343.49034Arutyunov, A. V.; Karamzin, Dmitry Yu.; Pereira, F. L. 3 2016 On surjective quadratic mappings. Zbl 1351.26023Arutyunov, A. V.; Zhukovskii, S. E. 3 2016 Investigation of regularity conditions in optimal control problems with geometric mixed constraints. Zbl 1334.49063Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L.; Silva, G. N. 2 2016 Equilibrium prices in an economic equilibrium model. Zbl 1363.91057Arutyunov, A. V.; Pavlova, N. G.; Shananin, A. A. 1 2016 On the continuity of inverse mappings for Lipschitz perturbations of covering mappings. Zbl 1352.54018Arutyunov, A. V.; Zhukovskiy, S. E. 1 2016 Some properties and applications of the Hausdorff distance. Zbl 1353.54017Arutyunov, A. V.; Vartapetov, S. A.; Zhukovskiy, S. E. 1 2016 Coincidence points principle for mappings in partially ordered spaces. Zbl 1305.54048Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 25 2015 Stability theorems for estimating the distance to a set of coincidence points. Zbl 1326.54042Arutyunov, A. V.; Avakov, E. R.; Zhukovskiy, S. E. 20 2015 Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points. Zbl 1336.49005Arutyunov, A. V. 14 2015 On some continuity properties of the measure Lagrange multiplier from the maximum principle for state constrained problems. Zbl 1342.49057Arutyunov, A. V.; Karamzin, D. Yu. 10 2015 On the solvability of implicit differential inclusions. Zbl 1309.47069Arutyunov, Aram; de Oliveira, Valeriano Antunes; Lobo Pereira, Fernando; Zhukovskiy, Evgeniy; Zhukovskiy, Sergey 8 2015 On the structure of the set of coincidence points. Zbl 1322.54026Arutyunov, A. V.; Gel’man, B. D. 7 2015 State constraints in impulsive control problems: Gamkrelidze-like conditions of optimality. Zbl 1331.49047Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L. 6 2015 Continuous dependence of coincidence points on a parameter. Zbl 1310.47082Arutyunov, Aram; Zhukovskiy, Sergey 3 2015 Maximum principle in an optimal control problem with equality state constraints. Zbl 1317.49025Arutyunov, A. V.; Karamzin, D. Yu. 1 2015 Approximation to solutions of linear control systems by compactly supported solutions. Zbl 1320.93048Arutyunov, A. V. 1 2015 Uniform estimates of distances to a coincidence point set. Zbl 1327.54037Avakov, E. R.; Arutyunov, A. V.; Zhukovskiy, S. E. 1 2015 On estimates for solutions of systems of convex inequalities. Zbl 1331.49018Arutyunov, A. V.; Zhukovskiy, S. E. 1 2015 Coincidence points of two maps. Zbl 1304.54070Arutyunov, A. V. 8 2014 The coincidence point problem for set-valued mappings and Ulam-Hyers stability. Zbl 1419.54046Arutyunov, A. V. 7 2014 Perturbation of solutions of the coincidence point problem for two mappings. Zbl 1318.54021Arutyunov, A. V.; Zhukovskiy, S. E. 5 2014 An investigation of smooth maps in a neighbourhood of an abnormal point. Zbl 1295.26014Avakov, E. R.; Arutyunov, A. V.; Karamzin, D. Yu. 5 2014 On coincidence points of mappings in partially ordered spaces. Zbl 1312.54018Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 15 2013 Coincidence points of set-valued mappings in partially ordered spaces. Zbl 1301.49041Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 15 2013 Equilibrium price as a coincidence point of two mappings. Zbl 1274.91292Arutyunov, A. V.; Zhukovskij, S. E.; Pavlova, N. G. 5 2013 Optimality conditions for 2-regular problems with nonsmooth objective functions. Zbl 1282.90173Arutyunov, A. V.; Izmailov, A. F.; Shvartsman, I. 1 2013 Properties of the minimum function in the quadratic problem. Zbl 1306.90114Arutyunov, A. V. 1 2013 Covering mappings and well-posedness of nonlinear Volterra equations. Zbl 1237.45003Arutyunov, A. V.; Zhukovskiy, E. S.; Zhukovskiy, S. E. 26 2012 Smooth abnormal problems in extremum theory and analysis. Zbl 1367.47065Arutyunov, A. V. 19 2012 Pontryagin’s maximum principle for constrained impulsive control problems. Zbl 1236.49046Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. 15 2012 Two problems of the theory of quadratic maps. Zbl 1275.15015Arutyunov, A. V. 6 2012 Properties of the Lagrange multipliers in the Pontryagin maximum principle for optimal control problems with state constraints. Zbl 1260.49026Arutyunov, A. V. 6 2012 An iterative method for finding coincidence points of two mappings. Zbl 1271.47053Arutyunov, A. V. 2 2012 Differential properties of the minimum function for diagonalizable quadratic problems. Zbl 1274.90219Arutyunov, A. V.; Zhukovskij, S. E.; Mingaleeva, Z. T. 1 2012 The maximum principle for optimal control problems with state constraints by R.V. Gamkrelidze: Revisited. Zbl 1221.49026Arutyunov, A. V.; Karamzin, D. Y.; Pereira, F. L. 34 2011 On the well-posedness of differential equations unsolved for the derivative. Zbl 1252.34009Arutyunov, A. V.; Zhukovskii, E. S.; Zhukovskii, S. E. 24 2011 On a generalization of the impulsive control concept: controlling system jumps. Zbl 1209.49048Arutyunov, Aram; Karamzin, Dmitry; Pereira, Fernando L. 15 2011 Regular zeros of quadratic maps and their application. Zbl 1232.26010Arutyunov, A. V.; Karamzin, D. Yu 11 2011 Existence of local solutions in constrained dynamic systems. Zbl 1232.93037Arutyunov, A. V.; Zhukovskiy, S. E. 10 2011 R.V. Gamkrelidze’s maximum principle for optimal control problems with bounded phase coordinates and its relation to other optimality conditions. Zbl 1253.49010Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. 3 2011 On constrained impulsive control problems. Zbl 1288.49013Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L. 18 2010 Existence and properties of inverse mappings. Zbl 1302.46010Arutyunov, A. V.; Zhukovskiy, S. E. 13 2010 Local solvability of control systems with mixed constraints. Zbl 1210.93026Arutyunov, A. V.; Zhukovskiy, S. E. 10 2010 Maximum principle in problems with mixed constraints under weak assumptions of regularity. Zbl 1221.49027Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. L. 8 2010 Pontryagin’s maximum principle for optimal impulsive control problems. Zbl 1205.49025Arutyunov, A. V.; Karamzin, D. Yu.; Pereira, F. 5 2010 On implicit function theorems at abnormal points. Zbl 1229.47098Arutyunov, A. V. 3 2010 Nikolai Alekseevich Izobov (a tribute in honor of his 70th birthday). Zbl 1191.01030Arutyunov, A. V.; Bibikov, Yu. N.; Emel’yanov, S. V.; Gaishun, I. V.; Il’in, V. A.; Kiguradze, I. T.; Korovin, S. K.; Kudryavtsev, L. D.; Kurzhanskii, A. B.; Makarov, E. K.; Martynyuk, A. A.; Mazanik, S. A.; Mishchenko, E. F.; Moiseev, E. I.; Osipov, Yu. S.; Pliss, V. A.; Rozov, N. Kh.; Sadovnichii, V. A.; Samoilenko, A. M.; Shemyakina, T. K.; Vasil’ev, F. P. 2 2010 Investigation of a linear optimal control problem with state constraints. Zbl 1211.49044Arutyunov, A. V.; Zhukov, D. 1 2010 Locally covering maps in metric spaces and coincidence points. Zbl 1182.54050Arutyunov, Aram; Avakov, Evgeniy; Gel’man, Boris; Dmitruk, Andrei; Obukhovskii, Valeri 49 2009 Stability of coincidence points and properties of covering mappings. Zbl 1186.54033Arutyunov, A. V. 41 2009 Covering mappings and their applications to differential equations unsolved for the derivative. Zbl 1204.54015Avakov, E. R.; Arutyunov, A. V.; Zhukovskii, E. S. 34 2009 Necessary optimality conditions for problems with equality and inequality constraints: Abnormal case. Zbl 1190.90263Arutyunov, A. V.; Karamzin, D. Y.; Pereira, F. L. 5 2009 New bifurcation theorems via the second-order optimality conditions. Zbl 1168.47050Arutyunov, A. V.; Izmailov, A. F.; Jaćimović, V. 4 2009 Stability of coincidence points and set-valued covering maps in metric spaces. Zbl 1192.54006Arutyunov, A. V. 2 2009 Minimum of a functional in a metric space and fixed points. Zbl 1224.58024Arutyunov, A. V.; Gel’man, B. D. 2 2009 Lagrange principle in quadratic optimal control problems with infinite horizon. Zbl 1187.49023Arutyunov, A. V. 1 2009 Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications. Zbl 1149.90140Arutyunov, A. V.; Avakov, E. R.; Izmailov, A. F. 10 2008 Nonnegativity of quadratic forms on intersections of quadrics and quadratic maps. Zbl 1219.90183Arutyunov, A. V. 5 2008 Exact penalties for optimization problems with 2-regular equality constraints. Zbl 1201.90160Avakov, E. R.; Arutyunov, A. V.; Izmailov, A. F. 1 2008 ...and 79 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 427 Authors 110 Arutyunov, Aram Vladimirovic 34 Zhukovskiĭ, Evgeniĭ Semenovich 33 Karamzin, Dmitry Yu. 33 Zhukovskiĭ, Sergeĭ Evgen’evich 26 Lobo Pereira, Fernando 23 Izmailov, Alekseĭ F. 17 Fomenko, Tat’yana Nikolaevna 14 Avakov, Evgeniĭ Rachievich 13 Staritsyn, Maksim Vladimirovich 12 Mordukhovich, Boris S. 11 Motta, Monica 10 Greshnov, Aleksandr Valer’evich 9 Aseev, Sergei M. 7 de Oliveira, Valeriano Antunes 7 Durea, Marius 7 Goncharova, Elena Vladimirovna 7 Nguyen Thi Toan 7 Samsonyuk, Ol’ga Nikolaevna 7 Shvartsman, Ilya A. 7 Solodov, Mikhail V. 7 Strugariu, Radu 6 Dykhta, Vladimir Aleksandrovich 6 Haeser, Gabriel 6 Huynh Van Ngai 6 Mardanov, Misir Dzhumail ogly 6 Podoprikhin, Dmitry A. 6 Rampazzo, Franco 6 Silva, Geraldo Nunes 6 Théra, Michel A. 6 Yao, Jen-Chih 6 Zhukovskaya, Tat’yana Vladimirovna 5 Andreani, Roberto 5 Becerril, Jorge A. 5 Benarab, Sarra 5 Dmitruk, Andrei V. 5 Fischer, Andreas 5 Fontes, Fernando A. C. C. 5 Frankowska, Hélène 5 Gfrerer, Helmut 5 Jaćimović, Vladimir 5 Magaril-Il’yaev, Gregoriĭ Geogrievich 5 Marinković, Boban 5 Merchela, Wassim 5 Obukhovskiĭ, Valeriĭ Vladimirovich 5 Osuna-Gómez, Rafaela 5 Rojas-Medar, Marko Antonio 5 Storozhuk, Konstantin Valer’evich 4 Aronna, María Soledad 4 Azhmyakov, Vadim 4 Cibulka, Radek 4 de Pinho, Maria do Rosário 4 Gel’man, Boris Danielovich 4 Hernández-Jiménez, Beatriz 4 Ioffe, Alexander Davidovich 4 Ledzewicz, Urszula 4 Malik, Samin T. 4 Mukhamedov, Farruh Maksutovich 4 Palladino, Michele 4 Pluzhnikova, Elena Aleksandrovna 4 Sorokin, Stepan Pavlovich 4 Thuy, Le Quang 4 Tron, Nguyen Huu 4 Vinter, Richard B. 3 Bettiol, Piernicola 3 Bianchi, Monica 3 Burlakov, Evgenii O. 3 Chernikova, Natalia Yu. 3 Colombo, Giovanni 3 Dontchev, Asen L. 3 Embong, Ahmad Fadillah 3 Ferreira, M. Margarida A. 3 Fusco, Giovanni 3 Gamkrelidze, Revaz Valerianovich 3 Gorokhovik, Valentin Vikent’evich 3 Hermosilla, Cristopher 3 Jelitte, Mario 3 Jović, Aleksandar 3 Kassay, Gábor 3 Kostyukova, Olga Ivanova 3 Melikov, Telman Kuli 3 Meng, Kaiwen 3 Merchela, Vassim 3 Mingaleeva, Z. T. 3 Pavlova, Natalia G. 3 Phan Quôc Khánh 3 Pini, Rita 3 Pogodaev, Nikolaĭ Il’ich 3 Poznyak, Aleksandr Semënovich 3 Rosenblueth, Javier F. 3 Roubal, Tomáš 3 Sadek, Ibrahim S. 3 Sartori, Caterina 3 Schättler, Heinz Michael 3 Schuverdt, María Laura 3 Uderzo, Amos 3 Vakhrameev, S. A. 3 Yang, Xiaoqi 3 Zhukovskaya, Zukhra Tagurovna 2 Adali, Sarp 2 Arguchintsev, Aleksandr Valer’evich ...and 327 more Authors all top 5 Cited in 122 Serials 51 Journal of Optimization Theory and Applications 34 Differential Equations 25 Set-Valued and Variational Analysis 22 Mathematical Notes 21 Doklady Mathematics 21 Proceedings of the Steklov Institute of Mathematics 19 Journal of Mathematical Sciences (New York) 17 Journal of Mathematical Analysis and Applications 15 Mathematical Programming. Series A. Series B 15 Vestnik Rossiĭskikh Universitetov. Matematika 13 Optimization 11 Nonlinear Analysis. Theory, Methods & Applications. 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