Minimax Theory and its Applications 07 (2022), No. 1, 119--130
Copyright Heldermann Verlag 2022
Approximate Solutions to Nonsmooth Multiobjective Programming Problems
Mohammad Golestani
Dept. of Mathematics, Fasa University, Fasa, Iran
golestani@fasau.ac.ir
We consider a multiobjective mathematical programming problem with inequality and equality constraints, where all functions are locally Lipschitz. An approximate strong Karush-Kuhn-Tucker (ASKKT for short) condition is defined and we show that every local efficient solution is an ASKKT point without any additional condition. Then a nonsmooth version of cone-continuity regularity is defined for this kind of problem. It is revealed that every ASKKT point under the cone-continuity regularity is a strong Karush-Kuhn-Tucker (SKKT for short) point. Correspondingly, the ASKKTs and the cone-continuity property are defined and the relations between them are investigated.
Keywords: Mathematical programming, optimality conditions, nonlinear programming, nonsmooth analysis and approximate conditions.
MSC: 90C46, 90C30, 90C29, 49J52.
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