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

• Verfasst von: Kanzow, Christian [VerfasserIn]
• Verfasst von: Petra, Stefania [VerfasserIn]
• Titel: Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems
• Verf.angabe: Christian Kanzow, Stefania Petra
• Jahr des Originals: 2007
• Umfang: 23 S.
• Fussnoten: Gesehen am 26.07.2018
• Titel Quelle: Enthalten in: Optimization methods & software
• Jahr Quelle: 2008
• Band/Heft Quelle: 22(2007), 5, S. 713-735
• ISSN Quelle: 1029-4937
• DOI: doi:10.1080/10556780701296455
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1577992644

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.