inexact proximal point

BILEVEL OPTIMIZATION AS A REGULARIZATION APPROACH TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

  • Bui Van Dinh
  • Le Dung Muu
  • Pham Gia Hung
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Global Optimization Tags , , , ,

    We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Un- like monotone case, in pseudomonotone case, the regularized subprob- lems may not be strongly monotone, even not pseudomonotone. How- ever, every proximal trajectory weakly converges to the same limit, We use these properties to extend … Read more

    Convergence rate of inexact proximal point methods with relative error criteria for convex optimization

  • Renato D.C. Monteiro
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    In this paper, we consider a class of inexact proximal point methods for convex optimization which allows a relative error tolerance in the approximate solution of each proximal subproblem. By exploiting the special structure of convex optimization problems, we are able to derive surprising complexity bounds for the aforementioned class. As a consequence, we show … Read more