Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems

Authors:
Christian Kanzow;Stefania Petra
Affiliations:
University of Würzburg, Institute of Mathematics, Würzburg, Germany;University of Würzburg, Institute of Mathematics, Würzburg, Germany
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

A reformulation of the mixed complementarity problem as a box constrained overdetermined system of semismooth equations or, equivalently, a box constrained nonlinear least squares problem with zero residual is presented. On the basis of this reformulation, a trust region method for the solution of mixed complementarity problems is considered. This trust region method contains elements from different areas: a projected Levenberg-Marquardt step in order to guarantee local fast convergence under suitable assumptions, affine scaling matrices which are used to improve the global convergence properties, and a multidimensional filter technique to accept a full step more frequently. Global convergence results as well as local superlinear/quadratic convergence is shown under appropriate assumptions. Moreover, numerical results for the MCPLIB indicate that the overall method is quite robust.