Aram Arutyunov

Idiomas

Áreas de atuação

Orientou

Produções bibliográficas

• ARUTYUNOV, A. . On two questions of optimization theory concerning quadratic mappings. Optimization Letters , v. 6, p. 1009-1015, 2012.

• Arutyunov, A.V. ; Zhukovskiy, S.E. . Covering mappings and well-posedness of nonlinear Volterra equations. Nonlinear Analysis , v. 75, p. 1026-1044, 2012.

• Arutyunov, A.V. ; ARUTYUNOV, A. ; Karamzin, D. ; PEREIRA, F. ; Karamzin, D.Yu. . Pontryagin s maximum principle for constrained impulsive control problems. Nonlinear Analysis , v. 75, p. 1045-1057, 2012.

• Arutyunov, A. V. ; Zhukovskii, E. S. ; Zhukovskii, S. E. . On the well-posedness of differential equations unsolved for the derivative. Differential Equations , v. 47, p. 1541-1555, 2011.

• Arutyunov, Aram V ; Karamzin, Dmitry Yu ; Arutyunov, A. V. . Regular zeros of quadratic maps and their application. Sbornik. Mathematics , v. 202, p. 783-806, 2011.

• Arutyunov, A.V. ; Zhukovskiy, S.E. . Existence of local solutions in constrained dynamic systems. Applicable Analysis , v. 90, p. 889-898, 2011.

• Arutyunov, A. V. ; Karamzin, D. Yu. ; Pereira, F. . R.V. Gamkrelidze s maximum principle for optimal control problems with bounded phase coordinates and its relation to other optimality conditions. Doklady. Mathematics (Print) , v. 83, p. 131-135, 2011.

• Arutyunov, A. V. ; Arutyunov, A. V. ; Karamzin, D. Yu. ; Karamzin, D. Y. ; Pereira, F. L. . The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited. Journal of Optimization Theory and Applications (Dordrecht. Online) , v. 149, p. 474-493, 2011.

• Arutyunov, A. V. . Example of a linear abnormal optimal control problem. Differential Equations , v. 46, p. 1786-1788, 2010.

• Arutyunov, A. V. ; Zhukovskiy, S. E. . Local solvability of control systems with mixed constraints. Differential Equations , v. 46, p. 1561-1570, 2010.

• Arutyunov, A. V. . On implicit function theorems at abnormal points. Proceedings of the Steklov Institute of Mathematics , v. 271, p. 18-27, 2010.

• Arutyunov, A. V. ; Karamzin, D. Yu. ; Pereira, F. . Pontryagin s maximum principle for optimal impulsive control problems. Doklady. Mathematics (Print) , v. 81, p. 418-421, 2010.

• Arutyunov, A. V. ; Zhukovskiy, S. E. . Existence and properties of inverse mappings. Proceedings of the Steklov Institute of Mathematics , v. 271, p. 12-22, 2010.

• Arutyunov, A.V. ; ARUTYUNOV, A. ; Karamzin, D. ; Pereira, F.L. ; Karamzin, D.Yu. . Maximum principle in problems with mixed constraints under weak assumptions of regularity. Optimization (Print) , v. 59, p. 1067-1083, 2010.

• ARUTYUNOV, A. ; Arutyunov, A. V. ; Karamzin, D. ; Karamzin, D. Yu. ; Pereira, F. L. . On constrained impulsive control problems. Journal of Mathematical Sciences (New York, N.Y.) , v. 165, p. 654-688, 2010.

• Arutyunov, A. V. . Lagrange principle in quadratic optimal control problems with infinite horizon. Differential Equations , v. 45, p. 1595-1601, 2009.

• Arutyunov, A.V. ; Izmailov, A.F. ; Ja imovi , V. . New bifurcation theorems via the second-order optimality conditions. Journal of Mathematical Analysis and Applications (Print) , v. 359, p. 752-764, 2009.

• Arutyunov, A. V. ; Gel man, B. D. . Minimum of a functional in a metric space and fixed points. Computational Mathematics and Mathematical Physics , v. 49, p. 1111-1118, 2009.

• Arutyunov, A. V. . Stability of coincidence points and properties of covering mappings. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 86, p. 153-158, 2009.

• Arutyunov, A. V. . Stability of coincidence points and set-valued covering maps in metric spaces. Doklady. Mathematics (Print) , v. 80, p. 555-557, 2009.

• Avakov, E. R. ; Arutyunov, A. V. ; Zhukovskii, E. S. . Covering mappings and their applications to differential equations unsolved for the derivative. Differential Equations , v. 45, p. 627-649, 2009.

• Arutyunov, Aram ; Avakov, Evgeniy ; Gel man, Boris ; Dmitruk, Andrei ; Obukhovskii, Valeri ; Arutyunov, A. V. . Locally covering maps in metric spaces and coincidence points. Journal of Fixed Point Theory and its Applications (Print) , v. 5, p. 105-127, 2009.

• Arutyunov, A. V. ; ARUTYUNOV, A. ; Karamzin, D. ; Karamzin, D. Y. ; Pereira, F. L. . Necessary Optimality Conditions for Problems with Equality and Inequality Constraints: Abnormal Case. Journal of Optimization Theory and Applications (Dordrecht. Online) , v. 140, p. 391-408, 2009.

• Arutyunov, A. V. . Nonnegativity of quadratic forms on intersections of quadrics and quadratic maps. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 84, p. 155-165, 2008.

• Arutyunov, A. V. ; Avakov, E. R. ; Izmailov, A. F. . Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications. Mathematical Programming , v. 114, p. 37-68, 2008.

• Avakov, E. R. ; Arutyunov, A. V. ; Izmailov, A. F. . Exact penalties for optimization problems with 2-regular equality constraints. Computational Mathematics and Mathematical Physics , v. 48, p. 346-353, 2008.

• Arutyunov, Aram V. ; Avakov, Evgeniy R. ; Izmailov, Alexey F. ; Arutyunov, A. V. . Directional Regularity and Metric Regularity. SIAM Journal on Optimization (Print) , v. 18, p. 810-833, 2007.

• Arutyunov, A. V. . Covering mappings in metric spaces and fixed points. Doklady. Mathematics (Print) , v. 76, p. 665-668, 2007.

• Avakov, E. R. ; Arutyunov, A. V. ; Izmailov, A. F. . Necessary conditions for an extremum in a mathematical programming problem. Proceedings of the Steklov Institute of Mathematics , v. 256, p. 2-25, 2007.

• Arutyunov, A. V. ; Karamzin, D. Yu. . Necessary optimality conditions for abnormal problems with geometric constraints. Computational Mathematics and Mathematical Physics , v. 47, p. 349-360, 2007.

• Arutyunov, A. V. . Controllability of nonlinear systems with constrained controls. Differential Equations , v. 42, p. 1515-1523, 2006.

• Arutyunov, Aram V. ; Izmailov, Alexey F. ; Arutyunov, A. V. . Directional Stability Theorem and Directional Metric Regularity. Mathematics of Operations Research , v. 31, p. 526-543, 2006.

• Arutyunov, A. V. ; Karamzin, D. Yu. . Necessary optimality conditions in an abnormal optimization problem with equality constraints. Computational Mathematics and Mathematical Physics , v. 46, p. 1293-1298, 2006.

• Avakov, E. R. ; Arutyunov, A. V. ; Izmailov, A. F. . Directional metric regularity of mappings and stability theorems. Doklady. Mathematics (Print) , v. 74, p. 473-476, 2006.

• Avakov, E. R. ; Arutyunov, A. V. ; Izmailov, A. F. . Necessary conditions for an extremum in 2-regular problems. Doklady. Mathematics (Print) , v. 73, p. 340-343, 2006.

• Arutyunov, A. V. ; Kruglova, E. V. . On the consistency of linear and quadratic systems. Computational Mathematics and Mathematical Physics , v. 46, p. 537-540, 2006.

• Arutyunov, A. V. . Implicit function theorem without a priori assumptions about normality. Computational Mathematics and Mathematical Physics , v. 46, p. 195-205, 2006.

• Arutyunov, Aram ; Pereira, Fernando Lobo ; Arutyunov, A. V. . Second-Order Necessary Optimality Conditions for Problems Without A Priori Normality Assumptions. Mathematics of Operations Research , v. 31, p. 1-12, 2006.

• ARUTYUNOV, A. ; Karamzin, D. ; Pereira, F. . A Nondegenerate Maximum Principle for the Impulse Control Problem with State Constraints. SIAM Journal on Control and Optimization (Print) , v. 43, p. 1812-1843, 2005.

• Avakov, E R ; Arutyunov, A V ; Arutyunov, A. V. . Inverse function theorem and conditions of extremum for abnormal problems with non-closed range. Sbornik. Mathematics , v. 196, p. 1251-1269, 2005.

• Arutyunov, A. V. . Implicit-Function Theorem on the Cone in a Neighborhood of an Irregular Point. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 78, p. 573-576, 2005.

• Arutyunov, Aram V. ; Izmailov, Alexey F. ; Arutyunov, A. V. . Sensitivity Analysis for Cone-Constrained Optimization Problems Under the Relaxed Constraint Qualifications. Mathematics of Operations Research , v. 30, p. 333-353, 2005.

• Arutyunov, A. V. . Covering of nonlinear maps on a cone in neighborhoods of irregular points. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 77, p. 447-460, 2005.

• ARUTYUNOV, A. ; Dykhta, V. ; Lobo Pereira, F. . Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions. Journal of Optimization Theory and Applications , v. 124, p. 55-77, 2005.

• Arutyunov, A V ; Arutyunov, A. V. . On real quadratic forms annihilating an intersection of quadrics. Russian Mathematical Surveys (Print) , v. 60, p. 157-158, 2005.

• ARUTYUNOV, A. ; Pereira, F. . Necessary optimality conditions without a priori normality assumptions. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 402, p. 727-731, 2005.

• ARUTYUNOV, A. . Necessary optimality conditions for discrete optimal control problems. Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika , v. 1, p. 43-48, 2005.

• Arutyunov, A. V. ; Karamzin, D. Yu. . Necessary Conditions for a Weak Minimum in an Optimal Control Problem with Mixed Constraints. Differential Equations , v. 41, p. 1532-1543, 2005.

• ARUTYUNOV, A. . On consistency of quadratic and bilinear systems. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 402, p. 295-297, 2005.

• ARUTYUNOV, A. . On the consistency of quadratic and bilinear systems. Doklady. Mathematics (Print) , v. 71, p. 370-372, 2005.

• Arutyunov, A. V. ; Pavlova, N. G. . Topological properties of attainability sets of linear systems. Differential Equations , v. 40, p. 1645-1648, 2004.

• Arutyunov, A.V. ; Izmailov, A.F. . Abnormal equality-constrained optimization problems: sensitivity theory. Mathematical Programming , v. 100, p. 333, 2004.

• Arutyunov, Aram V. ; Izmailov, Alexey F. ; Arutyunov, A. V. . Tangent vectors to a zero set at abnormal points. Journal of Mathematical Analysis and Applications (Print) , v. 289, p. 66-76, 2004.

• ARUTYUNOV, A. . Second-order sufficient conditions for infinite-dimensional optimization problems. Doklady. Mathematics (Print) , v. 70, p. 904-907, 2004.

• ARUTYUNOV, A. ; Avakov, E. R. . Abnormal problems with a nonclosed image. Doklady. Mathematics (Print) , v. 70, p. 924-927, 2004.

• ARUTYUNOV, A. ; Vinter, R. B. . A simple 'finite approximations' proof of the Pontryagin maximum principle under reduced differentiability hypotheses. Set-Valued Analysis , v. 12, p. 5-24, 2004.

• Arutyunov, A. V. . The Pontryagin Maximum Principle and Sufficient Optimality Conditions for Nonlinear Problems. Differential Equations , v. 39, p. 1671-1679, 2003.

• Arutyunov, A. V. ; Vinter, R. B. . A Finite-Dimensional Approximation Method in Optimal Control Theory. Differential Equations , v. 39, p. 1519-1528, 2003.

• ARUTYUNOV, A. ; Ja imovi , V. ; Pereira, F. . Second order necessary conditions for optimal impulsive control problems. Journal of Dynamical and Control Systems , v. 9, p. 131-153, 2003.

• ARUTYUNOV, A. . Inverse function theorem on cones in neighborhood of an abnormal point. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 389, p. 7-11, 2003.

• ARUTYUNOV, A. . Inverse function theorem on a cone in the neighborhood of an abnormal point. Doklady. Mathematics (Print) , v. 67, p. 149-152, 2003.

• Arutyunov, Aram V. ; Izmailov, Alexey F. . Positive Definiteness of Forms: Numerical Identification. SIAM Journal on Control and Optimization (Print) , v. 41, p. 1567-1585, 2002.

• Arutyunov, A. V. ; Burkov, V. N. ; Zalozhnev, A. Yu. ; Karamzin, D. Yu. . A problem of optimal distribution of resources over a set of independent operations. Automation and Remote Control , v. 63, p. 792-802, 2002.

• Arutyunov, A. V. . On necessary second-order conditions in optimal control problems. Differential Equations , v. 38, p. 1531-1540, 2002.

• Arutyunov, A. V. ; Jacimovic, V. . 2-Normal processes in controlled dynamical systems. Differential Equations , v. 38, p. 1081-1094, 2002.

• Arutyunov, A. V. . Positive quadratic forms on intersections of quadrics. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 71, p. 25-33, 2002.

• ARUTYUNOV, A. ; Burkov, V. N. ; Karamzin, D. Yu. ; Zalozhnev, A. Yu. . Optimal resources allocation over the set of independent operations. Avtomatika i Telemekhanika , v. 5, p. 108-119, 2002.

• ARUTYUNOV, A. ; Karamzin, D. Yu. . Relaxation and perturbation of optimal control problem with state constraints. Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika , v. 2, p. 31-35, 2002.

• Arutyunov, A. V. . Milyutin's Theorem in Linear-Quadratic Optimal Control Problems. Differential Equations , v. 37, p. 1627-1630, 2001.

• Arutyunov, Aram V. ; Izmailov, Alexey F. . Bifurcation Theorems via Second-Order Optimality Conditions. Journal of Mathematical Analysis and Applications (Print) , v. 262, p. 564-576, 2001.

• ARUTYUNOV, A. . Specific selections for set-valued mappings. Doklady. Mathematics (Print) , v. 63, p. 182-184, 2001.

• ARUTYUNOV, A. . Conditions for a high-order extremum and tangent vectors at an abnormal point. Doklady. Mathematics (Print) , v. 64, p. 381-384, 2001.

• Arutyunov, A. V. ; Chernikova, N. Yu. . On controllability of trajectories in state-constrained optimal control problems. Journal of Mathematical Sciences (New York, N.Y.) , v. 103, p. 664-669, 2001.

• ARUTYUNOV, A. . Special type selectors of set-valued mappings. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 377, p. 298-301, 2001.

• ARUTYUNOV, A. . High order necessary optimality conditions and tangent vectors in abnormal point. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 381, p. 586-590, 2001.

• ARUTYUNOV, A. . Second-order necessary conditions in optimal control problems. Doklady. Mathematics (Print) , v. 61, p. 158-161, 2000.

• ARUTYUNOV, A. . Calculation of the cone tangent to the image of a mapping at a singular point. Doklady. Mathematics (Print) , v. 62, p. 351-352, 2000.

• ARUTYUNOV, A. . Seconds order necessary condition for optimal control problems. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 371, p. 10-13, 2000.

• ARUTYUNOV, A. . Implicit function theorem as a realization of the Lagrange principle. Abnormal points. Sbornik. Mathematics , v. 191, p. 1-24, 2000.

• Arutyunov, A. V. . Properties of quadratic mappings. Vestnik Moskovskogo Universiteta , v. 15, p. 30-32, 1999.

• Arutyunov, A. V. . Regular zeros of a quadratic mapping and local controllability of nonlinear systems. Differential Equations , v. 35, p. 723-728, 1999.

• Arutyunov, A. V. . The Implicit Function Theorem and Abnormal Points. Doklady. Mathematics (Print) , v. 60, p. 231-234, 1999.

• Arutyunov, A. V. . Pontryagin's maximum principle in optimal control theory. Journal of Mathematical Sciences (New York, N.Y.) , v. 94, p. 1311-1365, 1999.

• Arutyunov, A. V. ; Okoulevitch, A. I. . Necessary optimality conditions for optimal control problems with intermediate constraints. Journal of Dynamical and Control Systems , v. 4, p. 49-58, 1998.

• Arutyunov, A. V. . Second-order conditions in extremal problems. The abnormal points. Transactions of the American Mathematical Society , v. 350, p. 4341-4365, 1998.

• Arutyunov, Aram V. ; Aseev, Sergei M. . Investigation of the Degeneracy Phenomenon of the Maximum Principle for Optimal Control Problems with State Constraints. SIAM Journal on Control and Optimization (Print) , v. 35, p. 930-952, 1997.

• Arutyunov, A.V. . Abnormal extremal problems and optimality conditions. Nonlinear Analysis , v. 30, p. 2461-2467, 1997.

• Arutyunov, A.V. . Optimality conditions in abnormal extremal problems. Systems & Control Letters (Print) , v. 27, p. 279-284, 1996.

• Arutyunov, A V ; Arutyunov, A. V. . Second-order conditions in extremal problems with finite-dimensional range. 2-normal maps. Izvestiya. Mathematics , v. 60, p. 39-65, 1996.

• Arutyunov, A. V. . To the theory of abnormal extremum problems with finite-dimentional image. Doklady Akademii Nauk. Rossijskaa Akademia Nauk , v. 348, p. 295-298, 1996.

• Arutyunov, A. V. . Nonnegativity of degenerated quadratic forms of the calculus of variations. Journal of Mathematical Sciences , v. 68, p. 125-163, 1994.

• Arutyunov, A. V. ; Silin, D. B. ; Zerkalov, L. G. . Maximum principle and second-order conditions for minimax problems of optimal control. Journal of Optimization Theory and Applications , v. 75, p. 521-533, 1992.

• Arutyunov, A. V. . Optimality conditions of higher order for abnormal minimization problems. Siberian Mathematical Journal , v. 33, p. 557-565, 1992.

• Arutyunov, A. V. . Properties of quadratic maps in a Banach space. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 50, p. 993-999, 1991.

• Arutyunov, A. V. . Perturbations of extremal problems with constraints and necessary optimality conditions. Journal of Soviet Mathematics , v. 54, p. 1342-1400, 1991.

• Arutyunov, A. V. . Numerical method of solving complete-dimensional optimal-control problems. Soviet journal of computer and systems sciences , v. 25, p. 147-154, 1987.

• Arutyunov, A. V. . Maximum principle in a problema with phase constraints. Soviet journal of computer and systems sciences , v. 23, p. 28-35, 1985.

• Arutyunov, A. V. . On sufficient pursuit conditions in the theory of differential games. Moscow University computational mathematics and cybernetics , v. 1, p. 65, 1982.

• Arutyunov, A. V. . Convex properties of the legendre transform. Mathematical Notes of the Academy of Sciences of the USSR (Cessou em 1991. Cont. 1067-9073 Mathematical Notes) , v. 28, p. 591-595, 1980.

• ARUTYUNOV, A. ; Tikhomirov V.M. ; Magaril-Ilyaev G.G. . The Pontryagin Maximum Principle. Proof and applications. Moscow: Faktorial, 2006. 142p .

• ARUTYUNOV, A. . Optimality conditions: Abnormal and Degenerate problems. , 2000. 299p .

• ARUTYUNOV, A. . Extremum conditions: Abnormal and Degenerate problems. Moscow: Faktorial, 1997. 254p .

• ARUTYUNOV, A. ; Karamzin, D. ; Pereira, F. . The maximum principle for optimal control problems with state constraints by R.V. Gamkrelidze. In: The 8th International ISAAC congress, 2011, Moscow. The 8th International ISAAC congress.

• ARUTYUNOV, A. ; Pereira, F. ; Karamzin, D. Yu. . Second order necessary optimality conditions for abnormal problems with equality and inequality constraints. In: 23rd European Conference on Operational Research, 2009, Bonn. 23rd European Conference on Operational Research, 2009.

• ARUTYUNOV, A. ; Karamzin, D. ; Pereira, F. . Pontryagin's maximum principle for impulsive control problems. In: International conference Differential Equations and Topology dedicated to the 100th anniversary of L.S. Pontryagin birth, 2008, Moscow. Differential Equations and Topology.

• ARUTYUNOV, A. ; Karamzin, D. . Necessary optimality conditions in abnormal extremum problems. In: International conference Extremal problems in complex and real analysis (EPCaRA 2007), 2007, Moscow. Extremal problems in complex and real analysis.

• ARUTYUNOV, A. ; Karamzin, D. . On necessary extremum conditions in abnormal problems. In: International conference Tikhonov and contemporary mathematics, 2006, Moscow. Tikhonov and contemporary mathematics. p. 21.

• ARUTYUNOV, A. ; Pereira, Fernando Lobo . Second-order necessary conditions for optimal impulsive control. In: IFAC, 2005. ) IFAC Proceedings Volumes. p. 483-488.

• ARUTYUNOV, A. ; Pereira, Fernando Lobo . Nondegenerate necessary conditions of optimality for problems without normality assumptions. In: 44th IEEE Conference on Decision and Control, 2005. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC'05, 2005. p. 7302-7307.

• ARUTYUNOV, A. ; Karamzin, D. ; Pereira, F. . On optimal impulsive control problem with vector measure under state constraints. In: International conference Control theory and theory of generalized solutions of Hamilton-Jacobi equations, 2005, Ekaterinburg. Control theory and theory of generalized solutions of Hamilton-Jacobi equations. p. 22-26.

• ARUTYUNOV, A. ; Pereira, Fernando Lobo ; Dykhta, V. . First and Second Order Necessary Conditions of Optimality for Impulsive Control Problems. In: IEEE Conference on Decision and Control, 2003. Proceedings of the IEEE Conference on Decision and Control. p. 6357-6362.

• ARUTYUNOV, A. ; Karamzin, Dmitry Yu ; Pereira, Fernando Lobo . Nondegenerate Necessary Conditions for Optimal Impulsive Control Problems with State Constraints. In: IEEE Conference on Decision and Control, 2003. Proceedings of the IEEE Conference on Decision and Control. p. 233-238.

• ARUTYUNOV, A. ; Pereira, Fernando Lobo ; Jacimovic, V. . Second order necessary conditions of optimality for impulsive control systems. In: IEEE Conference on Decision and Control, 2002. Proceedings of the IEEE Conference on Decision and Control. p. 1576-1581.

• ARUTYUNOV, A. . Degeneracy phenomenon in optimal control problems with state constraints. In: IEEE Conference on Decision and Control, 1997. Proceedings of the IEEE Conference on Decision and Control.

Projetos de pesquisa

• 2012 - Atual

  Mathematical methods for investigation of abnormal optimal control problems, Descrição: RFBR project number 12-01-00427-а. , Situação: Em andamento; Natureza: Pesquisa. , Integrantes: Aram Arutyunov - Coordenador / Karamzin, D. - Integrante / Sergey Zhukovskii - Integrante.

• 2012 - Atual

  Covering mappings in generalized metric spaces and fixed points, Descrição: Marie-Curie project PIIF-GA-2011-301177 funded by the European Seventh Framework Programme Marie Curie Actions. People. Marie Curie International Incoming Fellowship (IIF), 2012. Member of the team. Grant holder Sergey Zhukovskii. This project is aimed at: 1) Investigation of covering mappings properties. 2) Application of covering mappings theory to solvability, well-posedness and some other problems of functional, differential and difference equations. 3) Applications of covering mappings theory in optimization.. , Situação: Em andamento; Natureza: Pesquisa. , Integrantes: Aram Arutyunov - Integrante / Fernando Pereira - Integrante / Sergey Zhukovskii - Integrante.

• 2011 - 2012

  Fundamental mathematical models of behavior of economic agents in the medium-term forecast of Russian economic dynamics, Descrição: Russian Foundation for Basic Research (RFBR) project number 11-01-12084-офи-м-2011. , Situação: Concluído; Natureza: Pesquisa. , Integrantes: Aram Arutyunov - Integrante / Karamzin, D. Yu. - Integrante / Sergey Zhukovskii - Integrante / Alexander Shananin - Integrante.

• 2009 - 2011

  Abnormal optimal control problems and constrained extremum problems, Descrição: a grant from RFBR, www.rfbr.ru, project number 09-01-00619. . , Situação: Concluído; Natureza: Pesquisa.

• 2008 - 2010

  Extremum problems, best approximations and optimal recovery, Descrição: RFBR project number 08-01-00450-а. , Situação: Concluído; Natureza: Pesquisa. , Integrantes: Aram Arutyunov - Integrante / Zhukovskiy, S. E. - Integrante / Karamzin, D. - Integrante / Tikhomirov V.M. - Coordenador.

• 2005 - 2007

  Extremum theory and abnormal problems, control of dynamical systems, Descrição: a grant from the Russian Foundation of Basic Research, project number 05-01-00193. This research project was devoted to the theory of abnormal problems and the closely related theory of real quadratic maps. By saying ``abnormal problem'' we understand a classic optimization problem with constraints (say, a finite-dimensional) in which, however, the conventional regularity assumption at the point of minimum does not hold true. This implies that the derivative of the constraint function degenerates at the point of minimum. Then, the minimizer turns out to be a singular point of the constraint map. Such minimizers are also called abnormal. The interest of this theory is within various optimality conditions in the case of abnormal minimizers. Note that, for abnormal optimization problems, the classic Lagrange multiplier rule is not informative since it holds trivially true. Moreover, it is well known that the classic second-order necessary conditions do not hold for abnormal problems. Per se, ``abnormality'' means that the local linear approximation of a problem has a structure quite different of that of the initial nonlinear setting. This can be explained by the following fact: the statement of classic inverse function theorem is not true in a neighborhood of an abnormal point. Therefore, the question of inverse function theorems in the proximity of abnormal (singular) points of a smooth map (which is interesting in itself) becomes extremely crucial for the present theory and plays a major role in derivation of extremum conditions for abnormal minimizers.. , Situação: Concluído; Natureza: Pesquisa. , Integrantes: Aram Arutyunov - Coordenador / Karamzin, D. Yu. - Integrante / Izmailov, A. F. - Integrante / Pavlova, N. G. - Integrante / Magaril-Ilyaev G.G. - Integrante.

• 2002 - 2004

  Abnormal problems and controllability of dynamical systems, Descrição: a grant from the Russian Foundation for Basic Research, www.rfbr.ru, project number 02-01-00334 The activities of this project comprised: Derivation of new inverse functions and implicit functions theorems for convex cones. These results are extremely pertinent for abnormal points. Investigation of the convergence of numerical methods to find degenerate extremals for different classes of optimal control problems. Derivation of new (stronger) high order necessary optimality conditions for optimal control problems with impulses. Development of a sensitivity theory for abnormal optimization problems with equality type constraints. Analysis of impulsive control problem with vector-valued measures and derivation of Maximum Principle. . , Situação: Concluído; Natureza: Pesquisa. , Integrantes: Aram Arutyunov - Coordenador / Karamzin, D. - Integrante.

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