Le Dung Muu

On Equilibrium Problems Involving Strongly Pseudomonotone Bifunctions

  • Le Dung Muu
  • V. Quy Nguyen
    • Categories Generalized Convexity/Monoticity Tags , ,

    We study equilibrium problems with strongly pseudomonotone bifunctions in real Hilbert spaces. We show the existence of a unique solution. We then propose a generalized strongly convergent projection method for equilibrium problems with strongly pseudomonotone bifunctions. The proposed method uses only one projection without requiring Lipschitz continuity. Application to variational inequalities is discussed. Citation Institute … Read more

    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

    Algorithms for Bilevel Pseudomonotone Variational Inequality Problems

  • Bui Van Dinh
  • Le Dung Muu
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags , , , ,

    We propose easily implementable algorithms for minimizing the norm with pseudomonotone variational inequality constraints. This bilevel problem arises in the Tikhonov regularization method for pseudomonone variational inequalities. Since the solution set of the lower variational inequality is not given explicitly, the available methods of mathematical programming and variational inequality can not be applied directly. With … Read more

    On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

  • Bui Van Dinh
  • Le Dung Muu
    • Categories Convex and Nonsmooth Optimization Tags , ,

    We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo $\nabla$-monotonicity concept from $\nabla$-monotonicity and prove that under pseudo $\nabla$-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss … Read more

    On DC. optimization algorithms for solving minmax flow problems

  • Quang Thuy Le
  • Le Dung Muu
    • Categories Global Optimization Applications, Network Optimization

    We formulate minmax flow problems as a DC. optimization problem. We then apply a DC primal-dual algorithm to solve the resulting problem.The obtained computational results show that the proposed algorithm is efficient thanks to particular structures of the minmax flow problems. Citation 1. An L. T. H. and Tao P. D., The DC (Difference of … Read more