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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1007/s10140-005-0448-6

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1573-2878

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On Approximate KKT Condition and its Extension to 

Authors: Gabriel Haeser María Laura Schuverdt
Publish Date: 2011/01/21
Volume: 149, Issue: 3, Pages: 528-539
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Abstract

In this work we introduce a necessary sequential ApproximateKarushKuhnTucker 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 GárcigaOtero 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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