广义弧连通凸向量变分不等式与多目标规划解之间的关系
RELATIONSHIPS BETWEEN VECTOR VARIATIONAL-LIKE INEQUALITIES AND MULTI-OBJECTIVE PROGRAMMING INVOLVING GENERALIZED ARCWISE CONNECTED FUNCTIONS

本文研究了广义弧连通凸性条件下向量变分不等式与多目标规划解之间关系的问题.利用凸分析和非光滑分析的方法，引入了一类（ρ，b）-右可微弧连通函数的概念，并举例说明了这类广义凸函数的存在性.获得了（ρ，b）-右可微弧连通凸多目标规划的有效解或弱有效解与向量变分不等式解之间存在紧密关系的结果，推广了文献中凸性假设下的相应结论，本文所得成果是向量优化理论研究内容的丰富和深化.
This paper is devoted to the study of relationships between vector variationallike inequalities and multi-objective programming under the assumption of generalized arcwise connected convexities. By employing the methods in convex analysis and nonsmooth analysis, the notion of (ρ, b)-right differential arcwise connected functions are introduced, and then some examples are presented to illustrate their existences. It discloses the close relationships between the e-cient solutions or weakly e-cient solutions of (ρ, b)-right differential arcwise connected multiobjective programming and the solutions of vector variational-like inequalities, which generalize those conclusions in the case of convexity in literatures, enrich and deepen the theory of vector optimization