J. X. da Cruz Neto

Learning how to play Nash, potential games and alternating minimization method for structured nonconvex problems on Riemannian manifolds

  • J. X. da Cruz Neto
  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Pedro A. Soares Jr.
    • Categories Applications - Science and Engineering, Game Theory, Nonsmooth Optimization

    In this paper we consider minimization problems with constraints. We show that if the set of constaints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfi es the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We … Read more

    Proximal point method on Finslerian manifolds and the “Effort Accuracy Trade off”

  • J. X. da Cruz Neto
  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Pedro A. Soares Jr.
    • Categories Applications - Science and Engineering, Global Optimization Applications, Nonlinear Optimization

    In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove … Read more

    A new class of potential affine algorithms for linear convex programming

  • A. W. Martins Pinto
  • Paulo Roberto Oliveira
  • J. X. da Cruz Neto
    • Categories Convex Optimization Tags ,

    We obtain a new class of primal affine algorithms for the linearly constrained convex programming. It is constructed from a family of metrics generated the r power, r>=1, of the diagonal iterate vector matrix. We obtain the so called weak convergence. That class contains, as particular cases, the multiplicative Eggermont algorithm for the minimization of … Read more