Approximation of the whole Pareto optimal set for the vector optimization problem

Abstract

In multi-objective optimization problems several objective functions have to be minimized simultaneously. In this work, we present a new computational method for the linearly constrained, convex multi-objective optimization problem. We propose some techniques to find joint decreasing directions for both the unconstrained and the linearly constrained case as well. Based on these results, we introduce a method using a subdivision technique to approximate the whole Pareto optimal set of the linearly constrained, convex multi-objective optimization problem. Finally, we illustrate our algorithm by solving the Markowitz model on real data.