An explicit three-term Polak–Ribière–Polyak conjugate gradient method for bicriteria optimization

Abstract

A three-term Polak–Ribière–Polyak conjugate gradient-like method for bicriteria optimization without scalarization is proposed in this paper. Three advantages are to be noted. First, the descent directions are given explicitly and can then be directly computed. Second, the descent property turns out to be sufficient and independent of the line search. Third, without Lipschitzian hypotheses, global convergence towards Pareto stationary points is proved under an Armijo type condition. Numerical experiments including comparisons with other methods are also reported.