Accelerated Diagonal Steepest Descent Method for Unconstrained Multiobjective Optimization

Abstract

In this paper, we propose two methods for solving unconstrained multiobjective optimization problems. First, we present a diagonal steepest descent method, in which, at each iteration, a common diagonal matrix is used to approximate the Hessian of every objective function. This method works directly with the objective functions, without using any kind of a priori chosen parameters. It is proved that accumulation points of the sequence generated by the method are Pareto-critical points under standard assumptions. Based on this approach and on the Nesterov step strategy, an improved version of the method is proposed and its convergence rate is analyzed. Finally, computational experiments are presented in order to analyze the performance of the proposed methods.