F. G. M. Cunha

A Proximal Point Algorithm with phi-Divergence to Quasiconvex Programming

  • F. G. M. Cunha
    • Categories Generalized Convexity/Monoticity, Nonlinear Optimization Tags , ,

    We use the proximal point method with the phi-divergence given by phi(t) = t – log t – 1 for the minimization of quasiconvex functions subject to nonnegativity constraints. We establish that the sequence generated by our algorithm is well-defined in the sense that it exists and it is not cyclical. Without any assumption of … Read more

    Generalization of the primal and dual affine scaling algorithms

  • F. G. M. Cunha
  • João Xavier da Cruz Neto
  • Paulo Roberto Oliveira
  • A. W. Martins Pinto
    • Categories Convex Optimization, Linear Programming

    We obtain a class of primal ane scaling algorithms which generalize some known algorithms. This class, depending on a r-parameter, is constructed through a family of metrics generated by ��r power, r  1, of the diagonal iterate vector matrix. We prove the so-called weak convergence of the primal class for nondegenerate linearly constrained convex … Read more