F. S. Lima

A study of Liu-Storey conjugate gradient methods for vector optimization

  • Max L. N. Gonçalves
  • Leandro Fonseca Prudente
  • F. S. Lima
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    This work presents a study of Liu-Storey (LS) nonlinear conjugate gradient (CG) methods to solve vector optimization problems. Three variants of the LS-CG method originally designed to solve single-objective problems are extended to the vector setting. The first algorithm restricts the LS conjugate parameter to be nonnegative and use a sufficiently accurate line search satisfying … Read more

    Globally convergent Newton-type methods for multiobjective optimization

  • Max L. N. Gonçalves
  • Leandro Fonseca Prudente
  • F. S. Lima
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    We propose two Newton-type methods for solving (possibly) nonconvex unconstrained multiobjective optimization problems. The first is directly inspired by the Newton method designed to solve convex problems, whereas  the second uses  second-order information of the objective functions with ingredients of the steepest descent method.  One of the key points of our approaches  is to impose … Read more