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Haeser, Gabriel; Schuverdt, María Laura

On approximate KKT condition and its extension to continuous variational inequalities. (English) Zbl 1220.90130

J. Optim. Theory Appl. 149, No. 3, 528-539 (2011).
Summary: In this work, we introduce a necessary sequential approximate Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the approximate gradient projection condition (AGP) of Gárciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Cited in 20 Documents

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C46 Optimality conditions and duality in mathematical programming

Keywords:

optimality conditions; variational inequalities; constraint qualifications; practical algorithms
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References:

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