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