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

摘要

In the recent paper of Giorgi, Jim\'enez and Novo (J Optim Theory Appl171:70--89, 2016), the authors introduced the so-called approximateKarush-Kuhn-Tucker (AKKT) condition for smooth multiobjective optimizationproblems and obtained some AKKT-type necessary optimality conditions andsufficient optimality conditions for weak efficient solutions of such aproblem. In this note, we extend these optimality conditions to locallyLipschitz multiobjective optimization problems using Mordukhovichsubdifferentials. Furthermore, we prove that, under some suitable additionalconditions, an AKKT condition is also a KKT one.