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.

► We characterize different types of efficient points of linear VSIO problems.
► Characterizations in terms of cones involving the data and KKT conditions.
► Methodology based on identifying tangent cones at feasible points.
► Tangent cones only computable under (global or local) constraint qualifications.