约束锥扰动多目标规划锥有效解集的闭性和半连续性

本文研究拓扑向量空间中目标映射和约束映射均为连续,约束映射的约束锥为半连续的条件下,受扰动可达目标集的锥有效点集和锥弱有效点集的闭性、半连续性和锥半连续性.在此基础上,得到了约束锥扰动多目标规划问题的锥有效解集和锥弱有效解集的闭性和半连续性.

CLOSEDNESS AND SEMICONTINUITY OF CONE EFFICIENT SOLUTION SETS FOR MULTIOBJECTIVE PROGRAMMING UNDER CONSTRAINT CONE PERTURBATIONS

The paper studies the closedness, semicontinuity and cone semicontinuity of cone efficient point sets and cone weakly efficient point sets of the perturbed attainable objective sets when both the objective maps and constraint maps are continuous and the constraint cone is semicontinuous in topological vector spaces. On this basis, we obtain the closedness and semicontinuity of cone efficient solution sets and cone weakly efficient solution sets for multiobjective programming problem under constraint cone perturbations.