R. C. M. Silva

An inexact and nonmonotone proximal method for smooth unconstrained minimization

  • Sandra Augusta Santos
  • R. C. M. Silva
    • Categories Unconstrained Optimization

    An implementable proximal point algorithm is established for the smooth nonconvex unconstrained minimization problem. At each iteration, the algorithm minimizes approximately a general quadratic by a truncated strategy with step length control. The main contributions are: (i) a framework for updating the proximal parameter; (ii) inexact criteria for approximately solving the subproblems; (iii) a nonmonotone … Read more

    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