Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.This research was partially supported by MICINN of Spain, Grant MTM2011-29064-C03-02 and CONACYT of Mexico, Grant 55681. The first author is Partner Investigator in the Australian Research Council Discovery Project DP120100467