Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

Abstract In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) preordered by a not necessarily solid (and pointed) convex cone. It well-known that there are many examples ordering cone has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim consider Pareto-type solution concepts such optimization based on intrinsic core notion generalized interiority notion). We propose new Henig-type proper efficiency concept dilating cones which relatively (i.e., their cores nonempty). Using functionals from dual cone, we able characterize sets (weakly, properly) efficient solutions under certain convexity assumptions. Toward this end, employ separation theorems working considered setting.