Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems
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 m...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
15 Aug 2008
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| In: |
Optimization methods & software
Year: 2007, Jahrgang: 22, Heft: 5, Pages: 713-735 |
| ISSN: | 1029-4937 |
| DOI: | 10.1080/10556780701296455 |
| Online-Zugang: | Resolving-System, Volltext: http://dx.doi.org/10.1080/10556780701296455
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| Verfasserangaben: | Christian Kanzow, Stefania Petra |
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| 520 | |a 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. | ||
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| 650 | 4 | |a Cauchy step | |
| 650 | 4 | |a Complementarity problems | |
| 650 | 4 | |a Filter method | |
| 650 | 4 | |a Global convergence | |
| 650 | 4 | |a Nonlinear least squares reformulation | |
| 650 | 4 | |a Quadratic convergence | |
| 650 | 4 | |a Semismooth functions | |
| 650 | 4 | |a Trust region methods | |
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