quasiconvex programming

A Proximal Point Algorithm with Bregman Distances for Quasiconvex Optimization over the Positive Orthant

  • João Xavier da Cruz Neto
  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Sissy da S. Souza
    • Categories Generalized Convexity/Monoticity Tags , , ,

    We present an interior proximal point method with Bregman distance, whose Bregman function is separable and the zone is the interior of the positive orthant, for solving the quasiconvex optimization problem under nonnegative constraints. We establish the well-definedness of the sequence generated by our algorithm and we prove convergence to a solution point when the … Read more

    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