This article presents a stochastic dynamic Generalized Nash-Cournot model to describe the evolution of the natural gas markets. The major gas chain players are depicted including: producers, consumers, storage, and pipeline operators, as well as intermediate local traders. Our economic structure...

To consider existence of solutions to various optimization-related problems, we first develop some equivalent versions of invariant-point theorems. Next, they are employed to derive sufficient conditions for the solution existence for two general models of variational relation and inclusion...

The paper deals with equilibrium problems (EPs) with nonlinear convex constraints. First, EP is reformulated as a global optimization problem introducing a class of gap functions, in which the feasible set of EP is replaced by a polyhedral approximation. Then, an algorithm is given for solving...

We consider a general equilibrium problem under weak coercivity conditions in a finite-dimensional space setting. It appears such a condition provides convergence of the general penalty method without any monotonicity assumptions. We also show that the regularized version of the penalty method...

We consider various kinds of solutions to nonsmooth vector equilibrium problems with functional constraints. By using first and second-order approximations as generalized derivatives, we establish both necessary and sufficient optimality conditions. Our first-order conditions are shown to be...

Our purpose in this paper is to prove strong convergence theorem for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup and the set of solutions to a system of equilibrium problems in a real Hilbert space using a new iterative method. Finally, we...

In the present paper we discuss three methods for solving equilibrium-type fixed point problems. Concentrating on problems whose solutions possess some stability property, we establish convergence of these three proximal-like algorithms that promise a very high numerical tractability and...

This paper presents a new method for solving mathematical programs with equilibrium constraints. The approach uses a transformation of the original problem via Schur’s decomposition coupled with two separate formulations for modeling related absolute value functions. The first formulation,...

We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using...