On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

Gabriel Haeser () and María Laura Schuverdt ()
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Gabriel Haeser: University of São Paulo
María Laura Schuverdt: University of La Plata, CP 172

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 3, No 5, 528-539

Abstract: 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.

Keywords: Optimality conditions; Variational inequalities; Constraint qualifications; Practical algorithms (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10957-011-9802-x

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