Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints

Hui Huang () and Haole Zhu
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Hui Huang: Department of Mathematics, Yunnan University, Kunming 650091, China
Haole Zhu: Department of Mathematics, Yunnan University, Kunming 650091, China

Mathematics, 2022, vol. 10, issue 23, 1-18

Abstract: This paper discusses optimality conditions for Borwein proper efficient solutions of nonsmooth multiobjective optimization problems with vanishing constraints. A new notion in terms of contingent cone and upper directional derivative is introduced, and a necessary condition for the Borwein proper efficient solution of the considered problem is derived. The concept of ε proper Abadie data qualification is also introduced, and a necessary condition which is called a strictly strong stationary condition for Borwein proper efficient solutions is obtained. In view of the strictly strong stationary condition, convexity of the objective functions, and quasi-convexity of constrained functions, sufficient conditions for the Borwein proper efficient solutions are presented. Some examples are given to illustrate the reasonability of the obtained results.

Keywords: Borwein proper efficient solution; nonsmooth multiobjective optimization; stationary condition; Clarke subdifferential (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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