Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems

Authors:
Masakazu Kojima;Levent Tunç/el
Affiliations:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo 152-8552, Japan (e-mail: kojima@is.titech.ac.jp)/;Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (Corresponding author. e-mail: ltuncel@math.uwaterloo.ca
Venue:
Journal of Global Optimization
Year:
2002

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Abstract

General successive convex relaxation methods (SRCMs) can be used to compute the convex hull of any compact set, in an Euclidean space, described by a system of quadratic inequalities and a compact convex set. Linear complementarity problems (LCPs) make an interesting and rich class of structured nonconvex optimization problems. In this paper, we study a few of the specialized lift-and-project methods and some of the possible ways of applying the general SCRMs to LCPs and related problems.