A Graphic Search Based on Active Sets for Nonlinear Convex Multiple Objective Programming with Linear Constraints

The aim of this paper is to present an algorithm which makes possible the determination or approximation of the efficient set for a problem of nonlinear convex multiple objective programming, with linear constraints, based on the general idea of the active set methods in nonlinear programming. Along the process, the efficient set of the problem is delimited; giving the sections of its contour placed on the boundary of the feasible set, and those which lie in the interior of X. To this end, we calculate the initial and final points of each boundary section, using comparative static techniques, and approximate the interior sections.Although this algorithm is designed to solve problems with two variables, our aim in the future is to extend these results to the general case, even if this implies the impossibility to obtain a graphic representation of the efficient set.