Henig Efficiency in Vector Optimization with Nearly Cone-subconvexlike Set-valued Functions

Abstract

In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.

The linear scalarizations and Lagrange multipliers for vector optimization

“…近几十年来, 对于向量优化问题的理论研究除了各类解的概念外, 还包括各类解之间的关系, 特别 是多种真有效解之间的关系 (参见文献 [20][21][22]); 一定条件下 (弱) 有效解与各类真有效解的存在性研 究 (参见文献 [23][24][25][26]); 在凸性或广义凸性条件下的择一定理及其各类解的线性标量化和非凸条件下 的非线性标量化 (参见文献 [27][28][29][30][31][32][33]); 各类解的 Lagrange 乘子存在性定理、鞍点定理和对偶定理 (参 见文献 [34][35][36][37][38][39][40][41]) 等. 这些理论成果越来越多地发表在国际一流的重要期刊上.…”