On a semismooth least squares formulation of complementarity problems with gap reduction

• Verfasst von: Kanzow, Christian [VerfasserIn]
• Verfasst von: Petra, Stefania [VerfasserIn]
• Titel: On a semismooth least squares formulation of complementarity problems with gap reduction
• Verf.angabe: Christian Kanzow, Stefania Petra
• E-Jahr: 2008
• Jahr: 04 Feb 2008
• Jahr des Originals: 2004
• Umfang: 19 S.
• Fussnoten: Published online: 04 Feb 2008 ; Gesehen am 26.07.2018
• Titel Quelle: Enthalten in: Optimization methods & software
• Ort Quelle: London [u.a.] : Taylor & Francis, 1992
• Jahr Quelle: 2004
• Band/Heft Quelle: 19(2004), 5, Seite 507-525
• ISSN Quelle: 1029-4937
• DOI: doi:10.1080/10556780410001683096
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Complementarity problems
• Sach-SW: Global convergence
• Sach-SW: Nonlinear least squares reformulation
• Sach-SW: Quadratic convergence
• Sach-SW: Semismooth functions
• K10plus-PPN: 1577992296

Abstract

We present a nonsmooth least squares reformulation of the complementarity problem and investigate its convergence properties. The global and local fast convergence results (under mild assumptions) are similar to some existing equation-based methods. In fact, our least squares formulation is obtained by modifying one of these equation-based methods (using the Fischer-Burmeister function) in such a way that we overcome a major drawback of this equation-based method. The resulting nonsmooth Levenberg-Marquardt-type method turns out to be significantly more robust than the corresponding equation-based method. This is illustrated by our numerical results using the MCPLIB test problem collection.