Izmailov, A. F.; Solodov, M. V. Convergence rate estimates for penalty methods revisited. (English) Zbl 1522.90204 Comput. Optim. Appl. 85, No. 3, 973-992 (2023). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Comput. Optim. Appl. 85, No. 3, 973--992 (2023; Zbl 1522.90204) Full Text: DOI
Fischer, Andreas; Izmailov, Alexey F.; Jelitte, Mario Stability of singular solutions of nonlinear equations with restricted smoothness assumptions. (English) Zbl 1519.47062 J. Optim. Theory Appl. 196, No. 3, 1008-1035 (2023). MSC: 47J05 47J07 49J52 49J53 90C33 PDFBibTeX XMLCite \textit{A. Fischer} et al., J. Optim. Theory Appl. 196, No. 3, 1008--1035 (2023; Zbl 1519.47062) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Perturbed augmented Lagrangian method framework with applications to proximal and smoothed variants. (English) Zbl 1492.90172 J. Optim. Theory Appl. 193, No. 1-3, 491-522 (2022). MSC: 90C30 90C33 90C55 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, J. Optim. Theory Appl. 193, No. 1--3, 491--522 (2022; Zbl 1492.90172) Full Text: DOI
Izmailov, A. F. Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers. (English) Zbl 1482.90210 Comput. Optim. Appl. 80, No. 3, 943-978 (2021). MSC: 90C30 90C55 49M05 49M15 65K05 65K10 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Comput. Optim. Appl. 80, No. 3, 943--978 (2021; Zbl 1482.90210) Full Text: DOI
Fischer, A.; Izmailov, A. F.; Jelitte, M. Newton-type methods near critical solutions of piecewise smooth nonlinear equations. (English) Zbl 1487.65055 Comput. Optim. Appl. 80, No. 2, 587-615 (2021). MSC: 65H10 65K15 90C33 PDFBibTeX XMLCite \textit{A. Fischer} et al., Comput. Optim. Appl. 80, No. 2, 587--615 (2021; Zbl 1487.65055) Full Text: DOI
Fischer, A.; Izmailov, A. F.; Jelitte, M. Constrained Lipschitzian error bounds and noncritical solutions of constrained equations. (English) Zbl 1475.90110 Set-Valued Var. Anal. 29, No. 3, 745-765 (2021). MSC: 90C33 90C53 PDFBibTeX XMLCite \textit{A. Fischer} et al., Set-Valued Var. Anal. 29, No. 3, 745--765 (2021; Zbl 1475.90110) Full Text: DOI
Fischer, Andreas; Izmailov, Alexey F.; Scheck, Wladimir Adjusting dual iterates in the presence of critical Lagrange multipliers. (English) Zbl 1445.90105 SIAM J. Optim. 30, No. 2, 1555-1581 (2020). MSC: 90C30 90C55 65K05 PDFBibTeX XMLCite \textit{A. Fischer} et al., SIAM J. Optim. 30, No. 2, 1555--1581 (2020; Zbl 1445.90105) Full Text: DOI
Izmailov, A. F.; Solodov, M. V.; Uskov, E. I. A globally convergent Levenberg-Marquardt method for equality-constrained optimization. (English) Zbl 1411.90323 Comput. Optim. Appl. 72, No. 1, 215-239 (2019). MSC: 90C30 65K05 65K15 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Comput. Optim. Appl. 72, No. 1, 215--239 (2019; Zbl 1411.90323) Full Text: DOI
Fischer, Andreas; Izmailov, Alexey F.; Solodov, Mikhail V. Local attractors of Newton-type methods for constrained equations and complementarity problems with nonisolated solutions. (English) Zbl 1476.65116 J. Optim. Theory Appl. 180, No. 1, 140-169 (2019). MSC: 65K15 90C33 PDFBibTeX XMLCite \textit{A. Fischer} et al., J. Optim. Theory Appl. 180, No. 1, 140--169 (2019; Zbl 1476.65116) Full Text: DOI
Izmailov, Alexey F. (ed.); Lobo Pereira, Fernando (ed.); Mordukhovich, Boris S. (ed.) Preface: Nonlinear analysis and optimization. Special Issue dedicated to the 60th birthday of Professor Aram V. Arutyunov. (English) Zbl 1407.00036 J. Optim. Theory Appl. 180, No. 1, 1-4 (2019). MSC: 00B15 49-06 90-06 47-06 PDFBibTeX XMLCite \textit{A. F. Izmailov} (ed.) et al., J. Optim. Theory Appl. 180, No. 1, 1--4 (2019; Zbl 1407.00036) Full Text: DOI
Arutyunov, A. V.; Izmailov, A. F. Stability of possibly nonisolated solutions of constrained equations, with applications to complementarity and equilibrium problems. (English) Zbl 06913662 Set-Valued Var. Anal. 26, No. 2, 327-352 (2018). MSC: 47J05 49J53 90C33 PDFBibTeX XMLCite \textit{A. V. Arutyunov} and \textit{A. F. Izmailov}, Set-Valued Var. Anal. 26, No. 2, 327--352 (2018; Zbl 06913662) Full Text: DOI
Fischer, A.; Herrich, M.; Izmailov, A. F.; Scheck, W.; Solodov, M. V. A globally convergent LP-Newton method for piecewise smooth constrained equations: escaping nonstationary accumulation points. (English) Zbl 1415.90128 Comput. Optim. Appl. 69, No. 2, 325-349 (2018). MSC: 90C33 91A10 49M05 49M15 PDFBibTeX XMLCite \textit{A. Fischer} et al., Comput. Optim. Appl. 69, No. 2, 325--349 (2018; Zbl 1415.90128) Full Text: DOI
Izmailov, A. F.; Kurennoy, A. S.; Solodov, M. V. Critical solutions of nonlinear equations: stability issues. (English) Zbl 1396.90086 Math. Program. 168, No. 1-2 (B), 475-507 (2018). MSC: 90C33 65K10 49J53 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Math. Program. 168, No. 1--2 (B), 475--507 (2018; Zbl 1396.90086) Full Text: DOI
Izmailov, A. F.; Kurennoy, A. S.; Solodov, M. V. Critical solutions of nonlinear equations: local attraction for Newton-type methods. (English) Zbl 1404.90128 Math. Program. 167, No. 2 (A), 355-379 (2018). Reviewer: Samir Kumar Neogy (New Delhi) MSC: 90C33 65K10 49J53 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Math. Program. 167, No. 2 (A), 355--379 (2018; Zbl 1404.90128) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Some new facts about sequential quadratic programming methods employing second derivatives. (English) Zbl 1349.90764 Optim. Methods Softw. 31, No. 6, 1111-1131 (2016). MSC: 90C30 90C33 90C55 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Optim. Methods Softw. 31, No. 6, 1111--1131 (2016; Zbl 1349.90764) Full Text: DOI
Fischer, Andreas; Herrich, Markus; Izmailov, Alexey F.; Solodov, Mikhail V. A globally convergent LP-Newton method. (English) Zbl 1348.90583 SIAM J. Optim. 26, No. 4, 2012-2033 (2016). MSC: 90C33 91A10 49M05 49M15 PDFBibTeX XMLCite \textit{A. Fischer} et al., SIAM J. Optim. 26, No. 4, 2012--2033 (2016; Zbl 1348.90583) Full Text: DOI
Izmailov, A. F.; Solodov, M. V.; Uskov, E. I. Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty function. (English) Zbl 1360.65167 J. Optim. Theory Appl. 169, No. 1, 148-178 (2016). Reviewer: Nicolae Popovici (Cluj-Napoca) MSC: 65K05 90C20 90C55 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., J. Optim. Theory Appl. 169, No. 1, 148--178 (2016; Zbl 1360.65167) Full Text: DOI
Fischer, Andreas; Herrich, Markus; Izmailov, Alexey F.; Solodov, Mikhail V. Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions. (English) Zbl 1360.90247 Comput. Optim. Appl. 63, No. 2, 425-459 (2016). MSC: 90C33 90C53 PDFBibTeX XMLCite \textit{A. Fischer} et al., Comput. Optim. Appl. 63, No. 2, 425--459 (2016; Zbl 1360.90247) Full Text: DOI
Izmailov, A. F.; Kurennoy, A. S.; Solodov, M. V. Some composite-step constrained optimization methods interpreted via the perturbed sequential quadratic programming framework. (English) Zbl 1327.90313 Optim. Methods Softw. 30, No. 3, 461-477 (2015). MSC: 90C30 90C33 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Optim. Methods Softw. 30, No. 3, 461--477 (2015; Zbl 1327.90313) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Rejoinder on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it. (English) Zbl 1329.90139 Top 23, No. 1, 48-52 (2015). MSC: 90C30 90C33 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Top 23, No. 1, 48--52 (2015; Zbl 1329.90139) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it. (English) Zbl 1317.90279 Top 23, No. 1, 1-26 (2015). MSC: 90C30 90C33 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Top 23, No. 1, 1--26 (2015; Zbl 1317.90279) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Newton-type methods: a broader view. (English) Zbl 1310.65063 J. Optim. Theory Appl. 164, No. 2, 577-620 (2015). MSC: 65K05 90C20 90C30 90C53 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, J. Optim. Theory Appl. 164, No. 2, 577--620 (2015; Zbl 1310.65063) Full Text: DOI
Izmailov, A. F.; Kurennoy, A. S.; Solodov, M. V. Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption. (English) Zbl 1338.90408 Comput. Optim. Appl. 60, No. 1, 111-140 (2015). MSC: 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Comput. Optim. Appl. 60, No. 1, 111--140 (2015; Zbl 1338.90408) Full Text: DOI
Izmailov, Alexey; Solodov, Mikhail Optimization. Vol. 1. Conditions of optimality, elements of convex analysis and of duality. 3rd edition. (Otimização. Vol. 1. Condições de otimalidade, elementos de análise convexa e de dualidade.) (Portuguese) Zbl 1405.90001 Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (ISBN 978-85-244-0389-7). x, 274 p. (2014). MSC: 90-01 90Cxx 90-08 PDFBibTeX XMLCite \textit{A. Izmailov} and \textit{M. Solodov}, Otimização. Vol. 1. Condições de otimalidade, elementos de análise convexa e de dualidade (Portuguese). 3rd edition. Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (2014; Zbl 1405.90001)
Izmailov, Alexey F. Strongly regular nonsmooth generalized equations. (English) Zbl 1301.49043 Math. Program. 147, No. 1-2 (A), 581-590 (2014). MSC: 49J53 49J52 49K40 90C31 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Math. Program. 147, No. 1--2 (A), 581--590 (2014; Zbl 1301.49043) Full Text: DOI
Izmailov, Alexey F.; Solodov, Mikhail V. On error bounds and Newton-type methods for generalized Nash equilibrium problems. (English) Zbl 1307.91118 Comput. Optim. Appl. 59, No. 1-2, 201-218 (2014). MSC: 91A10 90C33 90C30 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Comput. Optim. Appl. 59, No. 1--2, 201--218 (2014; Zbl 1307.91118) Full Text: DOI
Izmailov, A. F.; Kurennoy, A. S. On regularity conditions for complementarity problems. (English) Zbl 1319.90068 Comput. Optim. Appl. 57, No. 3, 667-684 (2014). MSC: 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{A. S. Kurennoy}, Comput. Optim. Appl. 57, No. 3, 667--684 (2014; Zbl 1319.90068) Full Text: DOI
Izmailov, A. F.; Kurennoy, A. S. Abstract Newtonian frameworks and their applications. (English) Zbl 1298.49046 SIAM J. Optim. 23, No. 4, 2369-2396 (2013). Reviewer: Ctirad Matonoha (Prague) MSC: 49M15 65K05 65K10 90C30 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{A. S. Kurennoy}, SIAM J. Optim. 23, No. 4, 2369--2396 (2013; Zbl 1298.49046) Full Text: DOI Link
Izmailov, Alexey F.; Kurennoy, Alexey S.; Solodov, Mikhail V. A note on upper Lipschitz stability, error bounds, and critical multipliers for Lipschitz-continuous KKT systems. (English) Zbl 1282.90177 Math. Program. 142, No. 1-2 (A), 591-604 (2013). MSC: 90C30 90C55 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Math. Program. 142, No. 1--2 (A), 591--604 (2013; Zbl 1282.90177) Full Text: DOI
Izmailov, Alexey F.; Kurennoy, Alexey S.; Solodov, Mikhail V. The Josephy-Newton method for semismooth generalized equations and semismooth SQP for optimization. (English) Zbl 1285.90065 Set-Valued Var. Anal. 21, No. 1, 17-45 (2013). MSC: 90C30 90C55 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Set-Valued Var. Anal. 21, No. 1, 17--45 (2013; Zbl 1285.90065) Full Text: DOI
Izmailov, Alexey; Solodov, Mikhail Optimization. Vol. 2. Computational methods. 2nd edition. (Otimização. Vol. 2. Métodos computacionais.) (Portuguese) Zbl 1405.90002 Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (ISBN 978-85-244-0268-5). ix, 449 p. (2012). MSC: 90-01 90Cxx 90-08 PDFBibTeX XMLCite \textit{A. Izmailov} and \textit{M. Solodov}, Otimização. Vol. 2. Métodos computacionais (Portuguese). 2nd edition. Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (2012; Zbl 1405.90002)
Izmajlov, A. F.; Uskov, E. I. On the influence of the critical Lagrange multipliers on the convergence rate of the multiplier method. (Russian, English) Zbl 1274.90386 Zh. Vychisl. Mat. Mat. Fiz. 52, No. 11, 1959-1975 (2012); translation in Comput. Math. Math. Phys. 52, No. 11, 1504-1519 (2012). MSC: 90C30 PDFBibTeX XMLCite \textit{A. F. Izmajlov} and \textit{E. I. Uskov}, Zh. Vychisl. Mat. Mat. Fiz. 52, No. 11, 1959--1975 (2012; Zbl 1274.90386); translation in Comput. Math. Math. Phys. 52, No. 11, 1504--1519 (2012) Full Text: DOI
Izmajlov, A. F.; Kurennoj, A. S. Multiplier methods for optimization problems with Lipschitzian derivatives. (Russian, English) Zbl 1274.49043 Zh. Vychisl. Mat. Mat. Fiz. 52, No. 12, 2140-2148 (2012); translation in Comput. Math. Math. Phys. 52, No. 12, 1603-1611 (2012). MSC: 49M15 49L20 PDFBibTeX XMLCite \textit{A. F. Izmajlov} and \textit{A. S. Kurennoj}, Zh. Vychisl. Mat. Mat. Fiz. 52, No. 12, 2140--2148 (2012; Zbl 1274.49043); translation in Comput. Math. Math. Phys. 52, No. 12, 1603--1611 (2012) Full Text: DOI
Izmailov, A. F.; Solodov, M. V.; Uskov, E. I. Global convergence of augmented Lagrangian methods applied to optimization problems with degenerate constraints, including problems with complementarity constraints. (English) Zbl 1274.90385 SIAM J. Optim. 22, No. 4, 1579-1606 (2012). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 90C30 90C33 90C55 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., SIAM J. Optim. 22, No. 4, 1579--1606 (2012; Zbl 1274.90385) Full Text: DOI
Izmailov, A. F.; Pogosyan, A. L. Active-set Newton methods for mathematical programs with vanishing constraints. (English) Zbl 1284.90077 Comput. Optim. Appl. 53, No. 2, 425-452 (2012). MSC: 90C30 90C53 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{A. L. Pogosyan}, Comput. Optim. Appl. 53, No. 2, 425--452 (2012; Zbl 1284.90077) Full Text: DOI
Izmailov, A. F.; Pogosyan, A. L.; Solodov, M. V. Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints. (English) Zbl 1245.90124 Comput. Optim. Appl. 51, No. 1, 199-221 (2012). MSC: 90C30 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Comput. Optim. Appl. 51, No. 1, 199--221 (2012; Zbl 1245.90124) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Stabilized SQP revisited. (English) Zbl 1245.90145 Math. Program. 133, No. 1-2 (A), 93-120 (2012). MSC: 90C55 90C30 90C33 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Math. Program. 133, No. 1--2 (A), 93--120 (2012; Zbl 1245.90145) Full Text: DOI
Izmailov, A. F.; Uskov, E. I. On the application of Newton-type methods to Fritz John optimality conditions. (Russian, English) Zbl 1249.90254 Zh. Vychisl. Mat. Mat. Fiz. 51, No. 7, 1194-1208 (2011); translation in Comput. Math. Math. Phys. 51, No. 7, 1114-1127 (2011). MSC: 90C30 90C46 49M15 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{E. I. Uskov}, Zh. Vychisl. Mat. Mat. Fiz. 51, No. 7, 1194--1208 (2011; Zbl 1249.90254); translation in Comput. Math. Math. Phys. 51, No. 7, 1114--1127 (2011) Full Text: DOI
Izmailov, A. F.; Pogosyan, A. L. A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints. (Russian, English) Zbl 1249.90188 Zh. Vychisl. Mat. Mat. Fiz. 51, No. 6, 983-1006 (2011); translation in Comput. Math. Math. Phys. 51, No. 6, 919-941 (2011). MSC: 90C20 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{A. L. Pogosyan}, Zh. Vychisl. Mat. Mat. Fiz. 51, No. 6, 983--1006 (2011; Zbl 1249.90188); translation in Comput. Math. Math. Phys. 51, No. 6, 919--941 (2011) Full Text: DOI
Izmailov, A. F.; Pogosyan, A. L.; Solodov, M. V. Semismooth SQP method for equality-constrained optimization problems with an application to the lifted reformulation of mathematical programs with complementarity constraints. (English) Zbl 1254.90228 Optim. Methods Softw. 26, No. 4-5, 847-872 (2011). MSC: 90C30 90C33 90C55 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} et al., Optim. Methods Softw. 26, No. 4--5, 847--872 (2011; Zbl 1254.90228) Full Text: DOI
Izmailov, A. F. On the limiting properties of dual trajectories in the Lagrange multipliers method. (Russian, English) Zbl 1224.65154 Zh. Vychisl. Mat. Mat. Fiz. 51, No. 1, 3-23 (2011); translation in Comput. Math. Math. Phys. 51, No. 1, 1-20 (2011). MSC: 65K05 90C30 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Zh. Vychisl. Mat. Mat. Fiz. 51, No. 1, 3--23 (2011; Zbl 1224.65154); translation in Comput. Math. Math. Phys. 51, No. 1, 1--20 (2011) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. On attraction of linearly constrained Lagrangian methods and of stabilized and quasi-Newton SQP methods to critical multipliers. (English) Zbl 1218.90184 Math. Program. 126, No. 2 (A), 231-257 (2011). Reviewer: Stephan Dempe (Freiberg) MSC: 90C30 65K05 90C55 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Math. Program. 126, No. 2 (A), 231--257 (2011; Zbl 1218.90184) Full Text: DOI
Fernández, D.; Izmailov, A. F.; Solodov, M. V. Sharp primal superlinear convergence results for some Newtonian methods for constrained optimization. (English) Zbl 1235.90147 SIAM J. Optim. 20, No. 6, 3312-3334 (2010). Reviewer: Gabriela Cristescu (Arad) MSC: 90C30 90C33 90C55 65K05 PDFBibTeX XMLCite \textit{D. Fernández} et al., SIAM J. Optim. 20, No. 6, 3312--3334 (2010; Zbl 1235.90147) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. A truncated SQP method based on inexact interior-point solutions of subproblems. (English) Zbl 1211.90233 SIAM J. Optim. 20, No. 5, 2584-2613 (2010). MSC: 90C30 90C33 65K05 90C55 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, SIAM J. Optim. 20, No. 5, 2584--2613 (2010; Zbl 1211.90233) Full Text: DOI
Izmailov, A. F. Solution sensitivity for Karush-Kuhn-Tucker systems with non-unique Lagrange multipliers. (English) Zbl 1195.90084 Optimization 59, No. 5-6, 747-775 (2010). MSC: 90C31 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Optimization 59, No. 5--6, 747--775 (2010; Zbl 1195.90084) Full Text: DOI
Izmajlov, A. F.; Pogosyan, A. L. Optimality conditions and Newton-type methods for mathematical programs with vanishing constraints. (Russian, English) Zbl 1224.90165 Zh. Vychisl. Mat. Mat. Fiz. 49, No. 7, 1184-1196 (2009); translation in Comput. Math., Math. Phys. 49, No. 7, 1128-1140 (2009). MSC: 90C30 PDFBibTeX XMLCite \textit{A. F. Izmajlov} and \textit{A. L. Pogosyan}, Zh. Vychisl. Mat. Mat. Fiz. 49, No. 7, 1184--1196 (2009; Zbl 1224.90165); translation in Comput. Math., Math. Phys. 49, No. 7, 1128--1140 (2009) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. A survey on dual behavior of Newton-type methods for constrained optimization. (English) Zbl 1203.90147 Jaćimović, Milojica (ed.), Proceedings of the international conference on nonlinear analysis and optimization problems, Budva, Montenegro, October 6–10, 2008. Podgorica: Montenegrin Academy of Sciences and Arts (ISBN 978-86-7215-227-2/pbk). Scientific Meetings. Montenegrin Academy of Sciences and Arts 100; The Section of Natural Sciences 13, 157-174 (2009). MSC: 90C30 90C46 90C53 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, in: Proceedings of the international conference on nonlinear analysis and optimization problems, Budva, Montenegro, October 6--10, 2008. Podgorica: Montenegrin Academy of Sciences and Arts. 157--174 (2009; Zbl 1203.90147)
Izmailov, A. F. A new technique for avoiding the Maratos effect. (Russian) Zbl 1199.65205 Zh. Vychisl. Mat. Mat. Fiz. 49, No. 2, 241-254 (2009). Reviewer: Sergei Georgievich Zhuravlev (Moskva) MSC: 65K05 90C55 90C53 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Zh. Vychisl. Mat. Mat. Fiz. 49, No. 2, 241--254 (2009; Zbl 1199.65205)
Izmailov, A. F.; Solodov, M. V. Mathematical programs with vanishing constraints: Optimality conditions, sensitivity, and a relaxation method. (English) Zbl 1180.90312 J. Optim. Theory Appl. 142, No. 3, 501-532 (2009). Reviewer: Gerhard-Wilhelm Weber (Ankara) MSC: 90C30 90C46 90C31 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, J. Optim. Theory Appl. 142, No. 3, 501--532 (2009; Zbl 1180.90312) Full Text: DOI
Arutyunov, A. V.; Izmailov, A. F.; Jaćimović, V. New bifurcation theorems via the second-order optimality conditions. (English) Zbl 1168.47050 J. Math. Anal. Appl. 359, No. 2, 752-764 (2009). MSC: 47J15 49K27 90C46 PDFBibTeX XMLCite \textit{A. V. Arutyunov} et al., J. Math. Anal. Appl. 359, No. 2, 752--764 (2009; Zbl 1168.47050) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. An active-set Newton method for mathematical programs with complementarity constraints. (English) Zbl 1201.90193 SIAM J. Optim. 19, No. 3, 1003-1027 (2008). Reviewer: Serghey G. Suvorov (Donetsk) MSC: 90C33 90C30 49M37 65K10 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, SIAM J. Optim. 19, No. 3, 1003--1027 (2008; Zbl 1201.90193) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Numerical methods of optimization. 2nd revised ed. (Численные методы оптимизации.) (Russian) Zbl 1176.65074 Moskva: Fizmatlit (ISBN 978-5-9221-0975-8/hbk). 320 p. (2008). Reviewer: Nicolae Popovici (Cluj-Napoca) MSC: 65K05 90-01 90Cxx 65-02 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Численные методы оптимизации (Russian). 2nd revised ed. Moskva: Fizmatlit (2008; Zbl 1176.65074)
Avakov, E. R.; Arutyunov, A. V.; Izmailov, A. F. Necessary conditions for an extremum in a mathematical programming problem. (English. Russian original) Zbl 1160.49016 Proc. Steklov Inst. Math. 256, 2-25 (2007); translation from Tr. Mat. Inst. Steklova 256, 6-30 (2007). MSC: 49K10 90C30 90C46 90C48 PDFBibTeX XMLCite \textit{E. R. Avakov} et al., Proc. Steklov Inst. Math. 256, 2--25 (2007; Zbl 1160.49016); translation from Tr. Mat. Inst. Steklova 256, 6--30 (2007) Full Text: DOI
Daryina, A. N.; Izmailov, A. F. On the Newton-type method with admissible trajectories for mixed complementarity problems. (English. Russian original) Zbl 1126.49026 Autom. Remote Control 68, No. 2, 351-360 (2007); translation from Avtom. Telemekh. 68, No. 2, 152-161 (2007). MSC: 49M15 90C33 65K05 PDFBibTeX XMLCite \textit{A. N. Daryina} and \textit{A. F. Izmailov}, Autom. Remote Control 68, No. 2, 351--360 (2007; Zbl 1126.49026); translation from Avtom. Telemekh. 68, No. 2, 152--161 (2007) Full Text: DOI
Avakov, E. R.; Arutyunov, A. V.; Izmailov, A. F. Necessary conditions for an extremum in 2-regular problems. (English. Russian original) Zbl 1327.90375 Dokl. Math. 73, No. 3, 340-343 (2006); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 408, No. 2, 151-154 (2006). MSC: 90C46 90C30 PDFBibTeX XMLCite \textit{E. R. Avakov} et al., Dokl. Math. 73, No. 3, 340--343 (2006; Zbl 1327.90375); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 408, No. 2, 151--154 (2006) Full Text: DOI
Golishnikov, M. M.; Izmailov, A. F On attraction effect of Newton’s method towards critical Lagrange multipliers. (Russian) Zbl 1184.65064 Evtushenko, Yu. G. (ed.), Теоретические и прикладные задачи нелинейного анализа. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel’nyĭTsentr im. A. A. Dorodnitsyna (ISBN 5-201-09853-3). 23-38 (2006). MSC: 65K05 49M15 PDFBibTeX XMLCite \textit{M. M. Golishnikov} and \textit{A. F Izmailov}, in: Теоретические и прикладные задачи нелинейного анализа. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel'nyĭ Tsentr im. A. A. Dorodnitsyna. 23--38 (2006; Zbl 1184.65064)
Izmailov, A. F.; Shtutsa, V. Yu. A class of Newton’s methods for nonlinear complementary problems. (Russian) Zbl 1184.65065 Evtushenko, Yu. G. (ed.), Теоретические и прикладные задачи нелинейного анализа. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel’nyĭTsentr im. A. A. Dorodnitsyna (ISBN 5-201-09853-3). 3-22 (2006). MSC: 65K05 90C30 90C31 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{V. Yu. Shtutsa}, in: Теоретические и прикладные задачи нелинейного анализа. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel'nyĭ Tsentr im. A. A. Dorodnitsyna. 3--22 (2006; Zbl 1184.65065)
Daryina, A. N.; Izmailov, A. F. A strictly feasible Newton method for mixed complementarity problems. (English) Zbl 1115.90379 Grebenicov, E. (ed.) et al., CERMCS international conference of young scientists affiliated to the international conference on computer algebra in scientific computing 2006, (CASC 2006), Chişinău, Moldova, September 11–15, 2006. Communications. Chişinău: State University of Moldova, Centre of Education and Research in Mathematics and Computer Science, CERMCS; Chişinău: Tech. Univ. of Moldova (ISBN 978-9975-70-677-3/pbk). 38-43 (2006). MSC: 90C33 65K05 90C53 65K10 49J40 49M15 PDFBibTeX XMLCite \textit{A. N. Daryina} and \textit{A. F. Izmailov}, in: CERMCS international conference of young scientists affiliated to the international conference on computer algebra in scientific computing 2006, (CASC 2006), Chişinău, Moldova, September 11--15, 2006. Communications. Chişinău: State University of Moldova, Centre of Education and Research in Mathematics and Computer Science, CERMCS; Chişinău: Tech. Univ. of Moldova. 38--43 (2006; Zbl 1115.90379)
Izmailov, A. F.; Solodov, M. V. Primal error bounds based on the augmented Lagrangian and Lagrangian relaxation algorithms. (English) Zbl 1124.90032 Pac. J. Optim. 2, No. 3, 575-589 (2006). Reviewer: István Maros (Veszprem) MSC: 90C30 90C33 90C55 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Pac. J. Optim. 2, No. 3, 575--589 (2006; Zbl 1124.90032)
Daryina, A. N.; Izmailov, A. F.; Solodov, M. V. Numerical results for a globalized active-set Newton method for mixed complementarity problems. (English) Zbl 1213.90226 Comput. Appl. Math. 24, No. 2, 293-316 (2005). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{A. N. Daryina} et al., Comput. Appl. Math. 24, No. 2, 293--316 (2005; Zbl 1213.90226) Full Text: Link
Izmailov, A. F.; Shtutsa, M. Yu. A class of Newtonian methods for finding singular solutions of nonlinear equations under weakened methods smoothness requirements. (Russian) Zbl 1154.65330 Bereznev, V. A. (ed.), Теоретические и прикладные задачи нелинейного анализа. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel’nyĭ Tsentr im. A. A. Dorodnitsyna (ISBN 5-201-09836-3/pbk). 62-75 (2005). MSC: 65H10 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. Yu. Shtutsa}, in: Теоретические и прикладные задачи нелинейного анализа. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel'nyĭ Tsentr im. A. A. Dorodnitsyna. 62--75 (2005; Zbl 1154.65330)
Arutyunov, Aram V.; Izmailov, Alexey F. Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications. (English) Zbl 1082.90110 Math. Oper. Res. 30, No. 2, 333-353 (2005). MSC: 90C31 49K40 90C33 PDFBibTeX XMLCite \textit{A. V. Arutyunov} and \textit{A. F. Izmailov}, Math. Oper. Res. 30, No. 2, 333--353 (2005; Zbl 1082.90110) Full Text: DOI
Dar’ina, A. N.; Izmailov, A. F. On the identification of active indices in mixed complementarity problems. (Russian) Zbl 1154.90597 Berenzev, V. A. (ed.), Problems of modeling and analysis in decision making problems. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel’nyĭTsentr im. A. A. Dorodnitsyna (ISBN 5-201-09814-2/pbk). 72-87 (2004). MSC: 90C33 PDFBibTeX XMLCite \textit{A. N. Dar'ina} and \textit{A. F. Izmailov}, in: Вопросы моделирования и анализа в задачах принятия решений. Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel'nyĭ Tsentr im. A. A. Dorodnitsyna. 72--87 (2004; Zbl 1154.90597)
Izmailov, A. F. Optimization problems with complementary constraints: regularity, optimality conditions and sensibility. (Russian, English) Zbl 1085.49035 Zh. Vychisl. Mat. Mat. Fiz. 44, No. 7, 1209-1228 (2004); translation in Comput. Math. Math. Phys. 44, No. 7, 1145-1164 (2004). Reviewer: Andrei Zemskov (Moskva) MSC: 49K40 90C31 90C46 47H06 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Zh. Vychisl. Mat. Mat. Fiz. 44, No. 7, 1209--1228 (2004; Zbl 1085.49035); translation in Comput. Math. Math. Phys. 44, No. 7, 1145--1164 (2004)
Arutyunov, A. V.; Izmailov, A. F. Sensitivity analysis for abnormal optimization problems with a cone constraint. (Russian, English) Zbl 1114.90131 Zh. Vychisl. Mat. Mat. Fiz. 44, No. 4, 586-608 (2004); translation in Comput. Math. Math. Phys. 44, No. 4, 552-574 (2004). Reviewer: Andrei Zemskov (Moskva) MSC: 90C31 90C33 PDFBibTeX XMLCite \textit{A. V. Arutyunov} and \textit{A. F. Izmailov}, Zh. Vychisl. Mat. Mat. Fiz. 44, No. 4, 586--608 (2004; Zbl 1114.90131); translation in Comput. Math. Math. Phys. 44, No. 4, 552--574 (2004)
Daryina, A. N.; Izmailov, A. F.; Solodov, M. V. A class of active-set Newton methods for mixed complementarity problems. (English) Zbl 1077.90064 SIAM J. Optim. 15, No. 2, 409-429 (2004). MSC: 90C30 65K05 49M37 PDFBibTeX XMLCite \textit{A. N. Daryina} et al., SIAM J. Optim. 15, No. 2, 409--429 (2004; Zbl 1077.90064) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Newton-type methods for optimization problems without constraint qualifications. (English) Zbl 1106.90077 SIAM J. Optim. 15, No. 1, 210-228 (2004). MSC: 90C55 90C30 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, SIAM J. Optim. 15, No. 1, 210--228 (2004; Zbl 1106.90077) Full Text: DOI
Arutyunov, Aram V.; Izmailov, Alexey F. Tangent vectors to a zero set at abnormal points. (English) Zbl 1035.46043 J. Math. Anal. Appl. 289, No. 1, 66-76 (2004). MSC: 49J52 90C46 46N10 PDFBibTeX XMLCite \textit{A. V. Arutyunov} and \textit{A. F. Izmailov}, J. Math. Anal. Appl. 289, No. 1, 66--76 (2004; Zbl 1035.46043) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Numerical methods of optimization. (Chislennye metody optimizatsii.) (Russian. English summary) Zbl 1055.65075 Moskva: Fizmatlit (ISBN 5-9221-0045-9). 300 p. (2003). Reviewer: Nicolae Popovici (Cluj-Napoca) MSC: 65K05 90-01 90Cxx 65-02 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Chislennye metody optimizatsii (Russian). Moskva: Fizmatlit (2003; Zbl 1055.65075)
Arutyunov, Aram V.; Izmailov, Alexey F. Positive definiteness of forms: Numerical identification. (English) Zbl 1041.49021 SIAM J. Control Optimization 41, No. 5, 1567-1585 (2003). Reviewer: Ernst G. Al’brekht (Ekaterinburg) MSC: 49K15 49N10 65K05 PDFBibTeX XMLCite \textit{A. V. Arutyunov} and \textit{A. F. Izmailov}, SIAM J. Control Optim. 41, No. 5, 1567--1585 (2003; Zbl 1041.49021) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods. (English) Zbl 1023.90063 Math. Program. 95, No. 3 (A), 631-650 (2003). MSC: 90C30 90C53 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Math. Program. 95, No. 3 (A), 631--650 (2003; Zbl 1023.90063) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditions. (English) Zbl 1082.90136 Math. Oper. Res. 27, No. 3, 614-635 (2002). MSC: 90C46 46N10 49J52 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Math. Oper. Res. 27, No. 3, 614--635 (2002; Zbl 1082.90136) Full Text: DOI Link
Izmailov, A. F.; Solodov, M. V. Superlinearly convergent algorithms for solving singular equations and smooth reformulations of complementarity problems. (English) Zbl 1026.90085 SIAM J. Optim. 13, No. 2, 386-405 (2002). MSC: 90C33 46N10 90C30 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, SIAM J. Optim. 13, No. 2, 386--405 (2002; Zbl 1026.90085) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Complementarity constraint qualification via the theory of 2-regularity. (English) Zbl 1026.90084 SIAM J. Optim. 13, No. 2, 368-385 (2002). MSC: 90C33 90C30 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, SIAM J. Optim. 13, No. 2, 368--385 (2002; Zbl 1026.90084) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Optimality conditions for irregular inequality-constrained problems. (English) Zbl 1102.90376 SIAM J. Control Optim. 40, No. 4, 1280-1295 (2001). MSC: 90C46 47N10 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, SIAM J. Control Optim. 40, No. 4, 1280--1295 (2001; Zbl 1102.90376) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications. (English) Zbl 1023.90062 Math. Program. 89, No. 3 (A), 413-435 (2001). Reviewer: Mikhail Yu.Kokurin (Yoshkar-Ola) MSC: 90C30 49M30 65K05 46T20 90C33 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, Math. Program. 89, No. 3 (A), 413--435 (2001; Zbl 1023.90062) Full Text: DOI
Izmailov, A. F.; Solodov, M. V. The theory of 2-regularity for mappings with Lipschitz derivatives and its applications. (Russian) Zbl 1137.90716 Bereznev, V.A. (ed.) et al., Voprosy modelirovaniya i analiza v zadachakh prinyatiya reshenij. Moscow: RAN, Rossijskaya Akademiya Nauk, Vychislitel’nyj Tsentr (ISBN 5-201-09764-2). 26-50 (2000). MSC: 90C48 90C31 90C46 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{M. V. Solodov}, in: Voprosy modelirovaniya i analiza v zadachakh prinyatiya reshenij. Moscow: RAN, Rossijskaya Akademiya Nauk, Vychislitel'nyj Tsentr. 26--50 (2000; Zbl 1137.90716)
Izmailov, A. F.; Tret’yakov, A. A. On the gradient method in a Hilbert space in the case of nonisolated minima. (English. Russian original) Zbl 0964.90058 Comput. Math. Math. Phys. 39, No. 4, 521-524 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 4, 5459-552 (1999). MSC: 90C48 90C52 46N10 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{A. A. Tret'yakov}, Comput. Math. Math. Phys. 39, No. 4, 521--524 (1999; Zbl 0964.90058); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 4, 5459--552 (1999)
Izmailov, A. F. Optimality conditions in extremal problems with nonregular inequality constraints. (English. Russian original) Zbl 1016.90074 Math. Notes 66, No. 1, 72-81 (1999); translation from Mat. Zametki 66, No. 1, 89-101 (1999). MSC: 90C46 49K27 90C48 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Math. Notes 66, No. 1, 72--81 (1999; Zbl 1016.90074); translation from Mat. Zametki 66, No. 1, 89--101 (1999) Full Text: DOI
Izmailov, A. F.; Tret’yakov, A. A. Application of nonsmooth optimization methods to solving nonlinear operator equations. (English. Russian original) Zbl 0967.65071 Comput. Math. Math. Phys. 38, No. 9, 1391-1399 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 9, 1452-1460 (1998). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 65J15 47J25 90C52 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov} and \textit{A. A. Tret'yakov}, Comput. Math. Math. Phys. 38, No. 9, 1391--1399 (1998; Zbl 0967.65071); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 9, 1452--1460 (1998)
Izmailov, A. F. On the convergence of descent methods. (English. Russian original) Zbl 1030.90509 Comput. Math. Math. Phys. 38, No. 6, 866-874 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 6, 903-911 (1998). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 90C30 90C52 65K05 49M20 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Comput. Math. Math. Phys. 38, No. 6, 866--874 (1998; Zbl 1030.90509); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 6, 903--911 (1998)
Izmailov, A. F. On Lagrange methods for finding degenerate solutions of constrained extremum problems. (English. Russian original) Zbl 1161.90490 Comput. Math. Math. Phys. 36, No. 4, 423-429 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 4, 10-17 (1996). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{A. F. Izmailov}, Comput. Math. Math. Phys. 36, No. 4, 423--429 (1996; Zbl 1161.90490); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 4, 10--17 (1996)