Journal of Optimization Theory and Applications

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

Mathematical Programs with Complementarity Constraints in Banach Spaces



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.


Strong stationarity Mathematical program with complementarity constraints Polyhedricity Optimality conditions 

Mathematics Subject Classification

49K27 46N10 90C33 


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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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