A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints
| العنوان: | A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints |
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| المؤلفون: | Michael Ulbrich, Sonja Steffensen |
| المصدر: | SIAM Journal on Optimization. 20:2504-2539 |
| بيانات النشر: | Society for Industrial & Applied Mathematics (SIAM), 2010. |
| سنة النشر: | 2010 |
| مصطلحات موضوعية: | Nonlinear system, Mathematical optimization, Robustness (computer science), Complementarity theory, Test set, Limit point, Mathematics::Optimization and Control, Parameterized complexity, Mixed complementarity problem, Stationary point, Software, Theoretical Computer Science, Mathematics |
| الوصف: | We present a new relaxation scheme for mathematical programs with equilibrium constraints (MPEC), where the complementarity constraints are replaced by a reformulation that is exact for the complementarity conditions corresponding to sufficiently nondegenerate complementarity components and relaxes only the remaining complementarity conditions. A positive parameter determines to what extent the complementarity conditions are relaxed. The relaxation scheme is such that a strongly stationary solution of the MPEC is also a solution of the relaxed problem if the relaxation parameter is chosen sufficiently small. We discuss the properties of the resulting parameterized nonlinear programs and compare stationary points and solutions. We further prove that a limit point of a sequence of stationary points of a sequence of relaxed problems is Clarke-stationary if it satisfies a so-called MPEC-constant rank constraint qualification, and it is Mordukhovich-stationary if it satisfies the MPEC-linear independence constraint qualification and the stationary points satisfy a second order sufficient condition. From this relaxation scheme, a numerical approach is derived that is applied to a comprehensive test set. The numerical results show that the approach combines good efficiency with high robustness. |
| تدمد: | 1095-7189 1052-6234 |
| DOI: | 10.1137/090748883 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::3e07e87dfee32342ed48892f8dfadf8b https://doi.org/10.1137/090748883 |
| رقم الانضمام: | edsair.doi...........3e07e87dfee32342ed48892f8dfadf8b |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10957189 10526234 |
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| DOI: | 10.1137/090748883 |