An Explicit Three-Term Polak-Ribière-Polyak Conjugate Gradient Method for Bicriteria Optimization

We propose in this paper a Polak-Ribière-Polyak conjugate gradient type method for solving bicriteria optimization problems by avoiding scalarization techniques. Two particular advantages in this contribution are to be noted. First, the suggested descent direction common to both criteria may be directly computed by a given formula without solving any intermediate subproblem. Second, the descent property proves not only sufficient but also independent of the line search. The global convergence of the resulting algorithm towards (Pareto) critical points is guaranteed under standard hypotheses, while simply using appropriate Armijo-like stepsizes. Finally, numerical experiments including comparisons with another method of the same type are reported.


Hassan II University, Casablanca, Morocco, March 22, 2023.