On ε-Qptimality Conditions for Convex Semi-infinite Vector Optimization Problem

摘要

A convex semi-infinite vector optimization probelm (CSIVP), which consists of more than two convex objective functions and infinitely many convex constaint functions, is considered. We consider two kinds of ε-efficient solutions for (CSIVP), and to get optimality theorems for such solutions, we give a constraint qualification expressed with epigraphs of conjugate functions, which are weaker than the Slater condition. Under such a constraint qualification, we prove necessary and sufficient ε-optimality theorems for (CSIVP).