pareto critical point

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

    A Trust Region Algorithm for Heterogeneous Multiobjective Optimization

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization Tags , , , ,

    This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically … Read more

    The proximal point method for locally Lipschitz functions in multiobjective optimization

  • Glaydston Bento
  • João Xavier da Cruz Neto
  • Antoine Soubeyran
  • João Carlos Souza
  • G. López
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

    This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the … Read more

    A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Kely Diana Villacorta
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , , ,

    Multiobjective optimization has a significant number of real life applications. For this reason, in this paper, we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used by \citet{conn} to establish … Read more