A Simply Constrained Optimization Reformulation of KKT Systems Arising from Variational Inequalities |
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| Authors: | F Facchinei A Fischer C Kanzow J -M Peng |
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| Institution: | (1) Dipartimento di Informatica e Sistemistica, Università di Roma ``La Sapienza,' Via Buonarroti 12, I-00185 Roma, Italy soler@dis.uniroma1.it , IT;(2) Department of Mathematics, University of Dortmund, 44221 Dortmund, Germany fischer@math.uni-dortmund.de , DE;(3) Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany kanzow@math.uni-hamburg.de , DE;(4) State Key Laboratory of Scientific and Engineering Computing, Academia Sinica, P.O. Box 2719, Beijing, 100080, People's Republic of China pjm@lsec.cc.ac.cn , CN |
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| Abstract: | The Karush—Kuhn—Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained
optimization problems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose
casting KKT systems as a minimization problem with nonnegativity constraints on some of the variables. We prove that, under
fairly mild assumptions, every stationary point of this constrained minimization problem is a solution of the KKT conditions.
Based on this reformulation, a new algorithm for the solution of the KKT conditions is suggested and shown to have some strong
global and local convergence properties.
Accepted 10 December 1997 |
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| Keywords: | , KKT conditions, Variational inequalities, Constrained optimization problems, Global convergence, Quadratic convergence,,,,,,Semismoothness, Strong regularity, AMS Classification, 90C33, 90C30, |
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