A note on approximate Karush–Kuhn–Tucker conditions in locally Lipschitz multiobjective optimization
In the recent paper of Giorgi et al. (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.
KeywordsApproximate optimality conditions Multiobjective optimization problems Locally Lipschitz functions Mordukhovich subdifferential
The authors would like to thank the referees for their constructive comments which significantly improve the presentation of the paper. J.-C. Yao and C.-F. Wen are supported by the Taiwan MOST (Grant Nos. 106-2923-E-039-001-MY3, 106-2115-M-037-001), respectively, as well as the Grant from Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Taiwan.
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