Vector Duality for Linear and Semidefinite Vector Optimization Problems

Abstract

While the scalar linear optimization problems were intensively studied, inclusive via duality, and the things regarding them are settled down, the investigations on their vector counterparts are far from being complete. The first papers on linear vector duality were due to Gale, Kuhn and Tucker (cf. [96]), Kornbluth (cf. [150]), Schonefeld (cf. [187]) and Rodder (cf. [181]), while Isermann was the one who introduced in [132, 133] the classical vector dual problem to a primal linear vector optimization problem in finitely dimensional spaces. Moreover, he compared his results to the previously mentioned ones, pointing which of them could be recovered as special cases of his approach.