关键词: 多目标规划, 广义d_Ⅰ不变凸性, Ⅰ型一致不变凸, 最优充分性； 对偶

Abstract:

With the help of d_Ⅰinvexity, a new class of  concept of generalized d_Ⅰ-ⅤtypeⅠ univexity was introduced and a nondifferentiable multiobjective programming problem with inequality constraints was considered and some sufficient optimality conditions were derived under the assumptions of generalized d_Ⅰ-ⅤtypeⅠ univexity. Furthermore, a MondWeir type dual was formulated and weak duality, converse duality and strict duality theorems were proved.

Key words: multiobjective programming； generalized d_Ⅰinvexity； typeⅠ univexity； sufficient optimality； duality