集值优化问题的真有效性与向量似变分不等式

Proper Efficiency for Set-valued Optimization Problem and Vector Variational-like Inequalities

研究广义锥预不变凸集值映射优化问题(SVOP)的真有效解对的最优性条件。证明了(SVOP)的局部Henig有效解对也为全局Henig有效解对。获得了(SVOP)的Henig有效解对、超有效解对要满足的充分必要条件,同时建立了(SVOP)的真有效性与向量似变分不等式的真有效性之间的密切关系。

This paper studies proper efficiency in vector optimization involving generalized cone -preinvex set -valued mappings. Some properties of the generalized cone - preinvex mapping are derived, in particular, the global result for Henig efficient solution pair is proven, the necessary and sufficient optimality conditions of Henig efficiency and super efficiency are obtained. Meanwhile, we establish the closed relationships between proper efficiency of vector optimization and proper efficiency of vector variational - like inequalities.