Optimality, scalarization and duality in linear vector semi-infinite programming

In this paper, we introduce some qualification conditions for a linear vector semi-infinite programming problem. The new qualification conditions are used for development of necessary conditions for weak efficient, isolated efficient and ε-efficient solutions of such a problem. Sufficient conditions for the existence of such solutions are also provided. In addition, a new general scalarization technique for solving the reference problem is presented. Finally, we propose a type of Wolf dual problem and examine weakstrong duality relations.