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Journal of Optimization Theory and Applications

, Volume 166, Issue 2, pp 480–507 | Cite as

Mathematical Programs with Complementarity Constraints in Banach Spaces

  • Gerd WachsmuthEmail author
Article

Abstract

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.

Keywords

Strong stationarity Mathematical program with complementarity constraints Polyhedricity Optimality conditions 

Mathematics Subject Classification

49K27 46N10 90C33 

Notes

Acknowledgments

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics, Professorship Numerical Mathematics (Partial Differential Equations)Technische Universität ChemnitzChemnitzGermany

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