generalized proximal point methods

On the Convergence of the Entropy-Exponential Penalty Trajectories and Generalized Proximal Point Methods in Semidefinite Optimization

  • Orizon Pereira Ferreira
  • Paulo Roberto Oliveira
  • R. C. M. Silva
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , ,

    The convergence of primal and dual central paths associated to entropy and exponential functions, respectively, for semidefinite programming problem are studied in this paper. As an application, the proximal point method with the Kullback-Leibler distance applied to semidefinite programming problems is considered, and the convergence of primal and dual sequences is proved. CitationJournal of Global … Read more

    Central Paths in Semidefinite Programming, Generalized Proximal Point Method and Cauchy Trajectories in Riemannian Manifolds

  • João Xavier da Cruz Neto
  • Orizon Pereira Ferreira
  • Paulo Roberto Oliveira
  • R. C. M. Silva
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    The relationships among central path in the context of semidefinite programming, generalized proximal point method and Cauchy trajectory in Riemannian manifolds is studied in this paper. First it is proved that the central path associated to the general function is well defined. The convergence and characterization of its limit point is established for functions satisfying … Read more

    Dual Convergence of the Proximal Point Method with Bregman Distances for Linear Programming

  • João Xavier da Cruz Neto
  • Orizon Pereira Ferreira
  • Renato D.C. Monteiro
  • A. N. Iusem
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear Programming Tags , , , , , , ,

    In this paper we consider the proximal point method with Bregman distance applied to linear programming problems, and study the dual sequence obtained from the optimal multipliers of the linear constraints of each subproblem. We establish the convergence of this dual sequence, as well as convergence rate results for the primal sequence, for a suitable … Read more