A multiobjective interior primal-dual linear programming algorithm

Abstract

This paper presents an interior Multiobjective Linear Programming (MOLP) algorithm that is based on a variant of Karmarkar's interior-point algorithm known as the path-following primal-dual algorithm. The modification is accomplished by combining the single step direction vectors generated by the single-objective algorithm into a combined vector along which we step from the current iterate to the next iterate. Combining step direction vectors into a single step can be done by either approximating the gradient of an implicit utility function at the current iterate, or by creating convex combinations of single directions. We discuss both approaches and use the latter to develop an interior algorithm directed at handling MOLP problems. We refer to the resulting class of MOLP algorithms resulting from this variant as Primal-Dual Interior Multiobjective Linear Programming (PDIMOLP) algorithm.