A variational model for equilibrium problems in a traffic network

Hölder continuity of a parametric variational inequality

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

Different Network Performance Measures in a Multi-Objective Traffic Assignment Problem

Traffic assignment algorithms are used to determine possible use of paths between origin-destination pairs and predict traffic flow in network links. One of the main deficiencies of ordinary traffic assignment methods is that in most of them one measure (mostly travel time) is usually included in objective function and other effective performance measures in traffic assignment are not considere...

An Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...

The Equilibrium Equivalent Representation for Variational Inequalities Problems with Its Application in Mixed Traffic Flows

In this paper, we first introduce the relationship between the Hartman-Stampacchia variational inequalities (VI) problems and equilibrium programming (EP), and we present EP equivalent representation for Hartman-Stampacchia VI problems. After analyze and discuss the condition for optimization of EP, and the relation with the model transformation equivalent applied in mixed traffic assignment pr...

Strong convergence of a general implicit algorithm for variational inequality problems and equilibrium problems and a continuous representation of nonexpansive mappings

We introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems