1. On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization.
- Author
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Feng, Min, Li, Shengjie, and Wang, Jie
- Subjects
- *
NONSMOOTH optimization , *NONLINEAR systems , *GENERALIZATION - Abstract
This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present a generalization of Tucker's alternative theorem for conic nonlinear systems, provided that a closedness condition holds. Some sufficient conditions for the validity of such a closedness condition are given. As applications, under the weak Abadie regularity condition, we then establish the primal and the strong Karush/Kuhn–Tucker (dual) necessary optimality conditions for an efficient solution to be locally properly efficient in Borwein's sense. The primal and the dual conditions are formulated as an equivalent pair by means of the Tucker-type alternative results. Finally we give an example to illustrate that Borwein's locally properly efficient solution cannot be reduced to the only efficient one in the main results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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