Solving oligopolistic equilibrium problems with convex optimization

Solving inverse problems with overcomplete transforms and convex optimization techniques

Many algorithms have been proposed during the last decade in order to deal with inverse problems. Of particular interest are convex optimization approaches that consist of minimizing a criteria generally composed of two terms: a data fidelity (linked to noise) term and a prior (regularization) term. As image properties are often easier to extract in a transform domain, frame representations may...

Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data

Some Iterative Methods for Solving Equilibrium Problems and Optimization Problems

We introduce a new iterative scheme for finding a common element of the set of solutions of the equilibrium problems, the set of solutions of variational inequality for a relaxed cocoercive mapping, and the set of fixed points of a nonexpansive mapping. The results presented in this paper extend and improve some recent results of Ceng and Yao 2008 , Yao 2007 , S. Takahashi andW. Takahashi 2007 ...

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems

Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of a class of generalized Nash equilibrium problems (GNEPs). Further we give an unconstrained reformulation of a large subclass of all GNEPs which, in particular, includes the jointly convex GNEPs. Both approaches characterize all solutions of a GNEP as minima of optimization problems. Th...