关键词: 集值映射, 生成锥内部凸-锥-类凸性, Henig有效性, 鞍点, 对偶

Abstract:

In this paper, the set-valued vector optimization problems with constraint in locally convex spaces is studied. Under the assumption of the
ic-cone-convexlikeness, the optimality conditions for Henig proper efficient solutions are established in terms of scalarization and Lagrange multipliers. After introducing the new concept of Henig proper saddle-point for an appropriate set-valued Lagrange map, we use it to charactertize the Henig proper efficiency. In addition, a scalar Lagrange dual model for set-valued optimization is presented, and the dual theorems are obtained in sense of Henig proper efficiency. All the results   obtained in this paper are proven under the conditions that the constraint cone need not to have a nonempty interior.

Key words: Set-valued map, ic-cone-convexlikeness, Henig proper efficiency, Saddle-point, Duality