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A note on approximate Karush-Kuhn-Tucker conditions in locally Lipschitz multiobjective optimization

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arxiv 1711.08551 v2 pith:GWDV55FW submitted 2017-11-23 math.OC

A note on approximate Karush-Kuhn-Tucker conditions in locally Lipschitz multiobjective optimization

classification math.OC
keywords conditionsmultiobjectiveoptimalityoptimizationakktapproximateconditionkarush-kuhn-tucker
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In the recent paper of Giorgi, Jim\'enez and Novo (J Optim Theory Appl 171:70--89, 2016), the authors introduced the so-called approximate Karush-Kuhn-Tucker (AKKT) condition for smooth multiobjective optimization problems and obtained some AKKT-type necessary optimality conditions and sufficient optimality conditions for weak efficient solutions of such a problem. In this note, we extend these optimality conditions to locally Lipschitz multiobjective optimization problems using Mordukhovich subdifferentials. Furthermore, we prove that, under some suitable additional conditions, an AKKT condition is also a KKT one.

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