On Roughly Convex Multiobjective Optimization

期刊论文
发表日期：

2026年4月30日

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Tran Van Nghi,
Nguyen Van Tuyen

摘要

In this paper, we consider a roughly convex multiobjective optimization problem and use the concept of the outer $\gamma $ $γ$ -convexity (resp., the $\gamma $ $γ$ -convexlikeness) of the objective mapping, where $\gamma >0$ $γ > 0$ is the roughness degree of the objective one, to show that every $\gamma $ $γ$ -local weak efficient solution (resp., $\gamma $ $γ$ -local efficient solution) of the considered problem is also a global weak efficient one (resp., global efficient one). Necessary and sufficient conditions for efficiency solutions are established by using $\gamma $ $γ$ -subdifferentials. Examples are also given to illustrate the obtained results.