参数规划最优值函数的B-预不变凸凹性

B-preinvexity and B-preincavity Properties of Optimal Value Function in Parametric Programming

本文利用点到集映射图的概念,提出了一种新的不变凸(凹)点到集映射的概念,讨论了参数规划问题最优值函数的B-预不变凸凹性,研究了最优值函数的B-预不变凹性与其最优解集映射的不变凸性之间的关系,得到了若干新的结论,所得结果包含并推广了已有文献中的相关研究结果。

Based on the concept of point-to-set mapping graph, a new concept of an invex （incave） point-to-set map is presented. And, the B-preinvexity and B-preincavity of optimal value function in parametric programming are discussed. Some new results are obtained by the analysis of the rela- tionships between B-preincavity of optimal value function and preinvexity properties of the solution optimal sets mappings, our results generalize and improve some known results in literature.