An Explicit Spectral Fletcher-Reeves Conjugate Gradient Method for Bi-criteria Optimization

In this paper we propose a spectral Fletcher-Reeves conjugate gradient-like method (SFRCG) for solving unconstrained bi-criteria minimisation problems without using any technique of scalarization. We suggest an explicit formulae for computing a descent direction common to both criteria. This latter verifies furthermore a sufficient descent property which does not depend on the line search nor on any convexity hypothesis. After proving the existence of a bi-criteria Armijo-type stepsize, global convergence of the proposed algorithm is established. Finally, some numerical results and comparisons with other methods are reported.


Hassan II University, Casablanca, Morocco, October 12, 2022.