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Robust approximate optimality conditions for uncertain vector optimization problems and applications
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DOI：10.1007/s40314-026-03870-7.png)
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Abstract
En 中文
This paper presents novel optimality and duality characterizations for robust $$\epsilon $$ -quasi efficient solutions to uncertain vector optimization problems involving the intersection of closed sets. We introduce a generalized convexity notion in the sense of Clarke and establish its equivalent characterizations. A new version in the sense of Clarke of the robust constraint qualification (RCQ) is proposed. Then, we obtain necessary approximate optimality conditions for robust $$\epsilon $$ -quasi (weakly) efficient solutions of such problems. We also deduce sufficient approximate optimality conditions for robust $$\epsilon $$ -quasi efficient solutions of the uncertain vector optimization problem under suitable assumptions on the generalized convexity of the objective and constraint functions in the sense of Clarke. In addition, we introduce an approximate saddle point for the uncertain vector optimization problem involving the intersection of closed sets and explore the relationships between a robust $$\epsilon $$ -quasi saddle point and a robust $$\epsilon $$ -quasi Pareto efficient solution of that problem. As an application, we construct a Mixed-type uncertain dual problem for the original robust vector optimization problem and examine robust duality theorems for them.
Keywords:
Approximate efficient solutions
Robust constraint qualifications
Uncertain vector optimization problems
Clarke subdifferentials
Generalized convexity
Journal
C
IF:
2.5
Papers:
38
Citations:
0