Youssef Elboulqe

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

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , , , ,

    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 … Read more

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

  • Youssef Elboulqe
  • Mounir El Maghri
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    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 … Read more

    A Reduced Jacobian Scheme with Full Convergence for Multicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Constrained Nonlinear Optimization, Linear Programming, Multi-Criteria Optimization Tags , , , , ,

    In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe in [JOTA, 179 (2018) 917–943] for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant … Read more