次弧连通锥-凸集值优化问题近似解的最优性条件

Optimality of approximate solutions in set-valued optimization involving subarcwise connected cone-convexity

本文讨论相依上图导数形式下广义弧连通锥-凸集值优化近似解的最优性条件问题.首先,本文引入次弧连通锥-凸集值映射的概念,并举例说明次弧连通锥-凸性是弧连通锥-凸性的推广;其次,得到了次弧连通锥-凸集值映射的两个有用性质;最后,在次弧连通锥-凸性条件下,分别建立了集值优化问题强近似极小元和弱近似有效元的充分最优性条件.

This note deals with the optimality conditions of approximate solutions in set-valued optimization problems involving generalized arcwise connected convexity in terms of the contingent epiderivative. Firstly, the concept of subarcwise connected cone-convex set-valued mapping is introduced. Then, the two roperties of subarcwise connected cone-convex set-valued mapping are derived. Finally, the sufficient optimality conditions are established for weak approximate efficient and strong approximate efficient elements respectively under the assumption of subarcwise connected cone-convexity.