A Simply Constrained Optimization Reformulation of KKT Systems Arising from Variational Inequalities

Journal Article · Fri Jan 15 00:00:00 EST 1999 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900114· OSTI ID:21067548

Facchinei, F. ^[1]; Fischer, A. ^[2]; Kanzow, C. ^[3]; Peng, J.-M. ^[4]

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1. Dipartimento di Informatica e Sistemistica, Universita di Roma 'La Sapienza', Via Buonarroti 12, I-00185 Roma (Italy), E-mail: [e-mail]
2. Department of Mathematics, University of Dortmund, 44221 Dortmund (Germany), E-mail: [e-mail]
3. Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146 Hamburg (Germany), E-mail: [e-mail]
4. State Key Laboratory of Scientific and Engineering Computing, Academia Sinica, P.O. Box 2719, Beijing, 100080 (China), E-mail: [e-mail]

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.

• OSTI ID: 21067548
• Journal Information: Applied Mathematics and Optimization, Vol. 40, Issue 1; Other Information: DOI: 10.1007/s002459900114; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CONVERGENCE
MATHEMATICAL SOLUTIONS
MINIMIZATION
VARIATIONAL METHODS