RELATIONSHIPS BETWEEN VECTOR VARIATIONAL-LIKE INEQUALITIES AND MULTI-OBJECTIVE PROGRAMMING INVOLVING GENERALIZED ARCWISE CONNECTED FUNCTIONS
Xiaojun Ma, Guolin Yu, Sanyang Liu · 2018
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.