Surrogate duality for vector optimization

Abstract

Using our theorems (of [12]) on separation of convex sets by linear operators, in the sense of the lexi-cographical order on Rⁿ, we prove some theorems of surrogate duality for vector optimization problems with convex constraints (but no regularity assumption), where the surrogate constraint sets are generalized half-spaces and the surrogate multipliers are linear operators, or isomorphisms, or isometries. In the cae of inequality constraints, we prove that the surrogate multipliers can be taken lexicographically non-negative isometries or non-negative (in the usual order) linear isomorphisms.