Geometric Duality Results and Approximation Algorithms for Convex Vector Optimization Problems

We study geometric duality for convex vector optimization problems. For a primal problem with -dimensional objective space, we formulate dual space. Consequently, different from an existing approach, the does not depend on fixed direction parameter, and resulting image is cone. prove one-to-one correspondence between certain faces of images. In addition, show that polyhedral approximation one gives rise to other. Based this, propose algorithm which solves problems simultaneously free direction-biasedness. also modify direction-free in such way it as well. test performance algorithms randomly generated instances by using so-called error hypervolume indicator measures.