Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in findings ,, uch that is minimal in FA. To a family of vector minimization problems , one to an associates a Lagrange relation where belongs arbitrary class of mappings, the main purpose being to recover solutions of the original problem from the vector minimization of the Lagrange relation for an appropriate . This turns out to be a solution of a dual vector maximization problem. Characterizations of exact and approximate duality in terms of vector (generalized with respect to )convexity and subdifferentiability are given. They extend the thoery existing in scalar optimization. Verifiable criteria for exact penalities are also provided.
