Mathematical Programs with Complementarity Constraints in Banach Spaces
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We consider optimization problems in Banach spaces involving a complementarity constraint, defined by a convex cone K. By transferring the local decomposition approach, we define strong stationarity conditions and provide a constraint qualification, under which these conditions are necessary for optimality. To apply this technique, we provide a new uniqueness result for Lagrange multipliers in Banach spaces. In the case that the cone K is polyhedral, we show that our strong stationarity conditions possess a reasonable strength. Finally, we generalize to the case where K is not a cone and apply the theory to two examples.
KeywordsStrong stationarity Mathematical program with complementarity constraints Polyhedricity Optimality conditions
Mathematics Subject Classification49K27 46N10 90C33
The author would like to thank Radu Ioan Boţ for the idea leading to the counterexample at the end of Sect. 4.
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