On Approximate KKT Condition and its Extension to Continuous Variational Inequalities |
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Authors: | Gabriel Haeser María Laura Schuverdt |
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Institution: | (3) Royal Institute Technol. (KTH), Stockholm, Sweden; |
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Abstract: | 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. |
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Keywords: | |
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