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Kummer, Bernd

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 Author ID: kummer.bernd Published as: Kummer, B.; Kummer, Bernd External Links: MGP · Wikidata · GND
 Documents Indexed: 58 Publications since 1976, including 8 Books
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Co-Authors

 28 single-authored 24 Klatte, Diethard 6 Guddat, Jürgen 3 Bank, Bernd 3 Jongen, Hubertus Th. 3 Nožička, František 3 Tammer, Klaus 2 Schultz, Rüdiger 1 Bütikofer, Stephan 1 Fúsek, Peter 1 Grossman, Christian 1 Hollatz, Horst 1 Kall, Peter 1 Kruger, Alexander Ya. 1 Lommatzsch, Klaus 1 Straube, Bernd 1 Vlach, Milan 1 Zimmermann, Karel
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Serials

 5 Mathematical Programming. Series A. Series B 4 Seminarbericht, Humboldt-Universität zu Berlin, Sektion Mathematik 3 Optimization 2 Journal of Mathematical Analysis and Applications 2 Journal of Optimization Theory and Applications 2 Kybernetika 2 Mathematical Programming Study 2 Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin. Mathematisch-Naturwissenschaftliche Reihe 2 SIAM Journal on Optimization 1 Journal of the Australian Mathematical Society, Series B 1 Control and Cybernetics 1 Czechoslovak Mathematical Journal 1 Mathematische Operationsforschung und Statistik. Series Optimization 1 Annals of Operations Research 1 Wissenschaftliche Zeitschrift der Technischen Universität Dresden 1 ZOR. Zeitschrift für Operations Research 1 Computational Optimization and Applications 1 Journal of Mathematical Sciences (New York) 1 Journal of Convex Analysis 1 Vietnam Journal of Mathematics 1 Mathematical Methods of Operations Research 1 Discussiones Mathematicae. Differential Inclusions, Control and Optimization 1 Approximation and Optimization 1 ISNM. International Series of Numerical Mathematics 1 Nonconvex Optimization and Its Applications
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Fields

 49 Operations research, mathematical programming (90-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 8 Numerical analysis (65-XX) 5 General topology (54-XX) 4 General and overarching topics; collections (00-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Real functions (26-XX) 2 Combinatorics (05-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)

Citations contained in zbMATH

44 Publications have been cited 681 times in 526 Documents Cited by Year
Non-linear parametric optimization. Licensed ed. Zbl 0502.49002
Bank, B.; Guddat, J.; Klatte, D.; Kummer, B.; Tammer, K.
1983
Nonsmooth equations in optimization. Regularity, calculus, methods and applications. Zbl 1173.49300
Klatte, Diethard; Kummer, Bernd
2002
Newton’s method based on generalized derivatives for nonsmooth functions: Convergence analysis. Zbl 0768.49012
Kummer, Bernd
1992
Optimization methods and stability of inclusions in Banach spaces. Zbl 1158.49007
Klatte, Diethard; Kummer, Bernd
2009
Lipschitzian inverse functions, directional derivatives, and applications in $$C^{1,1}$$ optimization. Zbl 0795.49012
Kummer, B.
1991
Newton’s method for non-differentiable functions. Zbl 0662.65050
Kummer, Bernd
1988
Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland’s principle. Zbl 1165.49017
Kummer, Bernd
2009
An implicit-function theorem for $$C^{0,1}$$-equations and parametric $$C^{1,1}$$-optimization. Zbl 0742.49006
Kummer, Bernd
1991
Constrained minima and Lipschitzian penalties in metric spaces. Zbl 1042.49020
Klatte, Diethard; Kummer, Bernd
2002
From convergence principles to stability and optimality conditions. Zbl 1262.49020
Klatte, Diethard; Kruger, Alexander; Kummer, Bernd
2012
Strong Lipschitz stability of stationary solutions for nonlinear programs and variational inequalities. Zbl 1097.90058
Klatte, Diethard; Kummer, Bernd
2005
Generalized Newton and NCP-methods: Convergence, regularity, actions. Zbl 1016.90058
Kummer, Bernd
2000
Generalized equations: Solvability and regularity. Zbl 0568.49008
Kummer, Bernd
1984
Global stability of optimization problems. Zbl 0376.90083
Kummer, Bernd
1977
Metric regularity: Characterizations, nonsmooth variations and successive approximation. Zbl 0991.90125
Kummer, Bernd
1999
Approximations and generalized Newton methods. Zbl 1386.49022
Klatte, Diethard; Kummer, Bernd
2018
On calmness of the argmin mapping in parametric optimization problems. Zbl 1318.49030
Klatte, Diethard; Kummer, Bernd
2015
Aubin property and uniqueness of solutions in cone constrained optimization. Zbl 1269.49039
Klatte, Diethard; Kummer, Bernd
2013
Stability of inclusions: characterizations via suitable Lipschitz functions and algorithms. Zbl 1113.49028
Klatte, Diethard; Kummer, Bernd
2006
Lipschitzian and pseudo-Lipschitzian inverse functions and applications to nonlinear optimization. Zbl 0894.49013
Kummer, Bernd
1997
Generalized Kojima-functions and Lipschitz stability of critical points. Zbl 1017.90104
Klatte, Diethard; Kummer, Bernd
1999
Stability properties of infima and optimal solutions of parametric optimization problems. Zbl 0598.90083
Klatte, Diethard; Kummer, Bernd
1985
On the (Lipschitz-) continuity of solutions of parametric optimization problems. Zbl 0564.90071
Klatte, D.; Kummer, B.
1984
Stability and weak duality in convex programming without regularity. Zbl 0506.90069
Kummer, Bernd
1981
Globale Stabilität quadratischer Optimierungsprobleme. Zbl 0431.90060
Kummer, Bernd
1977
Parametrizations of Kojima’s system and relations to penalty and barrier functions. Zbl 0871.90086
Kummer, Bernd
1997
On solvability and regularity of a parametrized version of optimality conditions. Zbl 0834.90120
Kummer, Bernd
1995
Strong stability in nonlinear programming revisited. Zbl 0926.90084
Klatte, Diethard; Kummer, Bernd
1999
Approximation of multifunctions and superlinear convergence. Zbl 0899.49014
Kummer, Bernd
1995
Linearly and nonlinearly perturbed optimization problems in finite dimension. Zbl 0657.90092
Kummer, Bernd
1987
Stability of generalized equations and Kuhn-Tucker points of perturbed convex programs. Zbl 0562.90072
Kummer, B.
1984
Spiele auf Graphen. Zbl 0486.90086
Kummer, Bernd
1980
A note on the continuity of the solution set of special dual optimization problems. Zbl 0398.90093
Kummer, B.
1979
Correction to: “Approximations and generalized Newton methods”. Zbl 07152802
Klatte, Diethard; Kummer, Bernd
2020
Nonsmooth Kantorovich-Newton methods: hypotheses and auxiliary problems. Zbl 1427.49029
Klatte, Diethard; Kummer, Bernd
2019
On second-order Taylor expansion of critical values. Zbl 1197.65062
Bütikofer, Stephan; Klatte, Diethard; Kummer, Bernd
2010
Newton methods for stationary points: an elementary view of regularity conditions and solution schemes. Zbl 1149.90157
Klatte, Diethard; Kummer, Bernd
2007
Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ. Zbl 1249.90252
Grossman, Christian; Klatte, Diethard; Kummer, Bernd
2004
Examples and counterexamples in Lipschitz analysis. Zbl 1136.90480
Fusek, Peter; Klatte, Diethard; Kummer, Bernd
2002
Contingent derivatives of implicit (multi-) functions and stationary points. Zbl 0996.90076
Klatte, Diethard; Kummer, Bernd
2001
Inverse functions of pseudo regular mappings and regularity conditions. Zbl 1017.90112
Kummer, Bernd
2000
Lipschitz functions in a finite-dimensional space: The inverse and implicit functions, critical points in optimization problems, and methods of Newton type for solving Lipschitz equations (a survey). Zbl 0814.49013
Kummer, B.
1992
On stability and Newton-type methods for Lipschitzian equations with applications to optimization problems. Zbl 0798.90126
Kummer, Bernd
1992
Eine Einführung in die Theorie unscharfer Mengen. Zbl 0407.94020
Kummer, Bernd; Straube, Bernd
1977
Correction to: “Approximations and generalized Newton methods”. Zbl 07152802
Klatte, Diethard; Kummer, Bernd
2020
Nonsmooth Kantorovich-Newton methods: hypotheses and auxiliary problems. Zbl 1427.49029
Klatte, Diethard; Kummer, Bernd
2019
Approximations and generalized Newton methods. Zbl 1386.49022
Klatte, Diethard; Kummer, Bernd
2018
On calmness of the argmin mapping in parametric optimization problems. Zbl 1318.49030
Klatte, Diethard; Kummer, Bernd
2015
Aubin property and uniqueness of solutions in cone constrained optimization. Zbl 1269.49039
Klatte, Diethard; Kummer, Bernd
2013
From convergence principles to stability and optimality conditions. Zbl 1262.49020
Klatte, Diethard; Kruger, Alexander; Kummer, Bernd
2012
On second-order Taylor expansion of critical values. Zbl 1197.65062
Bütikofer, Stephan; Klatte, Diethard; Kummer, Bernd
2010
Optimization methods and stability of inclusions in Banach spaces. Zbl 1158.49007
Klatte, Diethard; Kummer, Bernd
2009
Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland’s principle. Zbl 1165.49017
Kummer, Bernd
2009
Newton methods for stationary points: an elementary view of regularity conditions and solution schemes. Zbl 1149.90157
Klatte, Diethard; Kummer, Bernd
2007
Stability of inclusions: characterizations via suitable Lipschitz functions and algorithms. Zbl 1113.49028
Klatte, Diethard; Kummer, Bernd
2006
Strong Lipschitz stability of stationary solutions for nonlinear programs and variational inequalities. Zbl 1097.90058
Klatte, Diethard; Kummer, Bernd
2005
Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ. Zbl 1249.90252
Grossman, Christian; Klatte, Diethard; Kummer, Bernd
2004
Nonsmooth equations in optimization. Regularity, calculus, methods and applications. Zbl 1173.49300
Klatte, Diethard; Kummer, Bernd
2002
Constrained minima and Lipschitzian penalties in metric spaces. Zbl 1042.49020
Klatte, Diethard; Kummer, Bernd
2002
Examples and counterexamples in Lipschitz analysis. Zbl 1136.90480
Fusek, Peter; Klatte, Diethard; Kummer, Bernd
2002
Contingent derivatives of implicit (multi-) functions and stationary points. Zbl 0996.90076
Klatte, Diethard; Kummer, Bernd
2001
Generalized Newton and NCP-methods: Convergence, regularity, actions. Zbl 1016.90058
Kummer, Bernd
2000
Inverse functions of pseudo regular mappings and regularity conditions. Zbl 1017.90112
Kummer, Bernd
2000
Metric regularity: Characterizations, nonsmooth variations and successive approximation. Zbl 0991.90125
Kummer, Bernd
1999
Generalized Kojima-functions and Lipschitz stability of critical points. Zbl 1017.90104
Klatte, Diethard; Kummer, Bernd
1999
Strong stability in nonlinear programming revisited. Zbl 0926.90084
Klatte, Diethard; Kummer, Bernd
1999
Lipschitzian and pseudo-Lipschitzian inverse functions and applications to nonlinear optimization. Zbl 0894.49013
Kummer, Bernd
1997
Parametrizations of Kojima’s system and relations to penalty and barrier functions. Zbl 0871.90086
Kummer, Bernd
1997
On solvability and regularity of a parametrized version of optimality conditions. Zbl 0834.90120
Kummer, Bernd
1995
Approximation of multifunctions and superlinear convergence. Zbl 0899.49014
Kummer, Bernd
1995
Newton’s method based on generalized derivatives for nonsmooth functions: Convergence analysis. Zbl 0768.49012
Kummer, Bernd
1992
Lipschitz functions in a finite-dimensional space: The inverse and implicit functions, critical points in optimization problems, and methods of Newton type for solving Lipschitz equations (a survey). Zbl 0814.49013
Kummer, B.
1992
On stability and Newton-type methods for Lipschitzian equations with applications to optimization problems. Zbl 0798.90126
Kummer, Bernd
1992
Lipschitzian inverse functions, directional derivatives, and applications in $$C^{1,1}$$ optimization. Zbl 0795.49012
Kummer, B.
1991
An implicit-function theorem for $$C^{0,1}$$-equations and parametric $$C^{1,1}$$-optimization. Zbl 0742.49006
Kummer, Bernd
1991
Newton’s method for non-differentiable functions. Zbl 0662.65050
Kummer, Bernd
1988
Linearly and nonlinearly perturbed optimization problems in finite dimension. Zbl 0657.90092
Kummer, Bernd
1987
Stability properties of infima and optimal solutions of parametric optimization problems. Zbl 0598.90083
Klatte, Diethard; Kummer, Bernd
1985
Generalized equations: Solvability and regularity. Zbl 0568.49008
Kummer, Bernd
1984
On the (Lipschitz-) continuity of solutions of parametric optimization problems. Zbl 0564.90071
Klatte, D.; Kummer, B.
1984
Stability of generalized equations and Kuhn-Tucker points of perturbed convex programs. Zbl 0562.90072
Kummer, B.
1984
Non-linear parametric optimization. Licensed ed. Zbl 0502.49002
Bank, B.; Guddat, J.; Klatte, D.; Kummer, B.; Tammer, K.
1983
Stability and weak duality in convex programming without regularity. Zbl 0506.90069
Kummer, Bernd
1981
Spiele auf Graphen. Zbl 0486.90086
Kummer, Bernd
1980
A note on the continuity of the solution set of special dual optimization problems. Zbl 0398.90093
Kummer, B.
1979
Global stability of optimization problems. Zbl 0376.90083
Kummer, Bernd
1977
Globale Stabilität quadratischer Optimierungsprobleme. Zbl 0431.90060
Kummer, Bernd
1977
Eine Einführung in die Theorie unscharfer Mengen. Zbl 0407.94020
Kummer, Bernd; Straube, Bernd
1977
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Cited by 583 Authors

 23 López-Cerdá, Marco Antonio 21 Cánovas, María Josefa 21 Parra, Juan 20 Mordukhovich, Boris S. 19 Klatte, Diethard 17 Kruger, Alexander Ya. 16 Outrata, Jiří V. 15 Dempe, Stephan 15 Kummer, Bernd 12 Gfrerer, Helmut 12 Goberna, Miguel Angel 12 Henrion, René 10 Dontchev, Asen L. 10 Izmailov, Alexey F. 10 Penot, Jean-Paul 9 Toledo, Fco. Javier 9 Zhang, Liwei 8 Qi, Liqun 8 Römisch, Werner 8 Schultz, Rüdiger 8 Sun, Defeng 8 Vera de Serio, Virginia N. 7 Hantoute, Abderrahim 7 Huynh Van Ngai 7 Solodov, Mikhail V. 7 Zheng, Xiyin 7 Zlobec, Sanjo 6 Bednarczuk, Ewa M. 6 Cibulka, Radek 6 Ioffe, Alexander Davidovich 6 Jongen, Hubertus Th. 6 Morgan, Jacqueline 6 Ng, Kung-Fu 5 Barton, Paul I. 5 Fischer, Andreas M. 5 Kanzow, Christian 5 Kurennoy, Alexey S. 5 Lee, Gue Myung 5 Mehlitz, Patrick 5 Thao, Nguyen Hieu 5 Uderzo, Amos 4 Adly, Samir 4 Chen, Zhiping 4 Clason, Christian 4 Durea, Marius 4 Hintermüller, Michael 4 Lignola, Maria Beatrice 4 Luke, D. Russell 4 Mitsos, Alexander 4 Páles, Zsolt 4 Sarabi, M. Ebrahim 4 Śmietański, Marek J. 4 Strugariu, Radu 4 Tam, Nguyen Nang 4 Théra, Michel A. 4 Van Ackooij, Wim 4 Vogel, Silvia 4 Weber, Gerhard-Wilhelm 4 Wei, Zhou 4 Yang, Xiaoqi 4 Yao, Jen-Chih 4 Ye, Jane J. 3 Aragón Artacho, Francisco Javier 3 Chen, Xiaojun 3 Chuong, Thai Doan 3 Dinh The Luc 3 Facchinei, Francisco 3 Fiacco, Anthony V. 3 Franke, Susanne 3 Gal, Tomas 3 Gaydu, Michaël 3 Geoffroy, Michel H. 3 Gisbert, María Jesús 3 Gómez-Senent, Francisco José 3 Han, Youpan 3 Herrich, Markus 3 Hoheisel, Tim 3 Huang, Nan-Jing 3 Ivanov Todorov, Maxim 3 Kunisch, Karl 3 Kyparisis, Jerzy 3 Mentagui, Driss 3 Pan, Shaohua 3 Phạm Tiên So’n 3 Phan Quôc Khánh 3 Pilecka, Maria 3 Poore, Aubrey B. 3 Rockafellar, Ralph Tyrrell 3 Rückmann, Jan-Joachim 3 Stein, Oliver 3 Tammer, Klaus 3 Toh, Kimchuan 3 Tseng, Paul 3 Xu, Huifu 3 Nguyen Dong Yen 3 Zeidan, Vera Michel 2 Aboussoror, Abdelmalek 2 Amaya, Jorge 2 Anh, Lam Quoc 2 Arutyunov, Aram Vladimirovic ...and 483 more Authors
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Cited in 98 Serials

 60 Mathematical Programming. Series A. Series B 52 Journal of Optimization Theory and Applications 28 SIAM Journal on Optimization 28 Set-Valued and Variational Analysis 26 Optimization 23 Journal of Mathematical Analysis and Applications 23 Computational Optimization and Applications 21 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 21 Journal of Global Optimization 15 European Journal of Operational Research 14 Mathematical Methods of Operations Research 11 Optimization Letters 10 Annals of Operations Research 9 Set-Valued Analysis 8 Kybernetika 7 Journal of Computational and Applied Mathematics 7 Numerical Functional Analysis and Optimization 7 Vietnam Journal of Mathematics 6 Automatica 6 ZOR. Zeitschrift für Operations Research 5 Computers & Mathematics with Applications 5 Applied Mathematics and Computation 5 Mathematics of Operations Research 5 Mathematical Programming 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Numerische Mathematik 4 Operations Research Letters 4 Top 4 Journal of Convex Analysis 4 Optimization Methods & Software 3 Aplikace Matematiky 3 Transactions of the American Mathematical Society 3 Mathematical Problems in Engineering 3 Journal of Industrial and Management Optimization 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applicable Analysis 2 Discrete Applied Mathematics 2 Applied Mathematics and Optimization 2 Computing 2 Journal of Mathematical Economics 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 SIAM Journal on Control and Optimization 2 OR Spektrum 2 Linear Algebra and its Applications 2 Applied Mathematics. Series B (English Edition) 2 RAIRO. Operations Research 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 SIAM Journal on Imaging Sciences 2 Science China. Mathematics 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Engineering Mathematics 1 Mathematical Notes 1 Stochastics 1 Mathematics of Computation 1 BIT 1 Fuzzy Sets and Systems 1 Information Sciences 1 International Journal of Game Theory 1 Journal of Approximation Theory 1 Journal of Economic Theory 1 Journal of Soviet Mathematics 1 Mathematische Nachrichten 1 Proceedings of the American Mathematical Society 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Computers & Operations Research 1 Numerical Methods for Partial Differential Equations 1 Journal of Economic Dynamics & Control 1 Applied Mathematics Letters 1 Queueing Systems 1 Computational Mathematics and Modeling 1 Japan Journal of Industrial and Applied Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 Automation and Remote Control 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Zeitschrift für Operations Research. Serie A: Theorie 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Electronic Communications in Probability 1 Mathematical Finance 1 Positivity 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 CEJOR. Central European Journal of Operations Research 1 International Game Theory Review 1 The ANZIAM Journal 1 Foundations of Computational Mathematics 1 Journal of the Australian Mathematical Society 1 Decisions in Economics and Finance 1 Journal of Applied Mathematics 1 Journal of Applied Mathematics and Computing 1 Central European Journal of Mathematics 1 4OR 1 Proceedings of the Steklov Institute of Mathematics 1 Mathematical Control and Related Fields 1 Journal of Computational Dynamics 1 SIAM/ASA Journal on Uncertainty Quantification
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Cited in 32 Fields

 417 Operations research, mathematical programming (90-XX) 253 Calculus of variations and optimal control; optimization (49-XX) 91 Numerical analysis (65-XX) 37 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 36 Operator theory (47-XX) 26 General topology (54-XX) 18 Functional analysis (46-XX) 18 Global analysis, analysis on manifolds (58-XX) 17 Real functions (26-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Convex and discrete geometry (52-XX) 9 Systems theory; control (93-XX) 7 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 6 Mechanics of deformable solids (74-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Information and communication theory, circuits (94-XX) 3 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 2 Mathematical logic and foundations (03-XX) 2 Combinatorics (05-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Algebraic geometry (14-XX) 2 Partial differential equations (35-XX) 2 Algebraic topology (55-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX)

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