Optimality Conditions for Disjunctive Programs with Application to Mathematical Programs with Equilibrium Constraints |
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Authors: | Michael L. Flegel, Christian Kanzow Ji í V. Outrata |
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Affiliation: | (1) Institute of Mathematics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany;(2) Academy of Sciences, Institute of Information Theory and Automation, 18208 Prague, Czech Republic |
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Abstract: | We consider optimization problems with a disjunctive structure of the feasible set. Using Guignard-type constraint qualifications for these optimization problems and exploiting some results for the limiting normal cone by Mordukhovich, we derive different optimality conditions. Furthermore, we specialize these results to mathematical programs with equilibrium constraints. In particular, we show that a new constraint qualification, weaker than any other constraint qualification used in the literature, is enough in order to show that a local minimum results in a so-called M-stationary point. Additional assumptions are also discussed which guarantee that such an M-stationary point is in fact a strongly stationary point. |
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Keywords: | disjunctive programs mathematical programs with equilibrium constraints M-stationarity strong stationarity Guignard constraint qualification |
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