A novel hybrid conjugate gradient method for multiobjective optimization problems

Abstract

In this paper, we propose a hybrid nonlinear conjugate gradient method with the strong Wolfe line search step-size rule to find the Pareto critical point of a multiobjective optimization problem. The novelty of our multiobjective conjugate gradient method (in short, MCGM) lies in that it uses a hybrid parameter β k CD − DY which is combined the CD parameter β k CD with the DY parameter β k DY introduced by Lucambio Pérez and Prudente. The global convergence of the proposed hybrid nonlinear MCGM is established under mild assumptions. Numerical experiments demonstrate the effectiveness of the proposed method.