On Equilibrium Problems Involving Strongly Pseudomonotone Bifunctions

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


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

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

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

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