This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of  upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on $f$ used in the literature are relaxed. The KKM technique is used to generalize and unify some exist...

Abstract We study relations between the solution sets of Variational Inequalities, Minty Natural Map problems and Nash Equilibrium Problems. Moreover, motivated by inherent relevance inexactness both in modeling non-cooperative games algorithms for variational inequalities, we consider inexact versions such establish to quantify how propagates from one problem other.

We propose a linesearch projection algorithm for solving non-monotone and non-Lipschitzian equilibrium problems in Hilbert spaces. It is proved that the sequence generated by proposed converges strongly to solution of problem under assumption set associated Minty nonempty. Compared with existing methods, we do not employ Fejér monotonicity strategy proving convergence. This comes from projectin...

We provide a new mathematical model for strategic traac management, formulated and analyzed as a mathematical program with equilibrium constraints (MPEC). The model includes two types of control (upper-level) variables, which may be used to describe such traac management actions as traac signal setting, network design, and congestion pricing. The lower-level problem of the MPEC describes a traa...

We provide a new mathematical model for strategic traffic management, formulated and analyzed as a mathematical program with equilibrium constraints (MPEC). The model includes two types of control (upper-level) variables, which may be used to describe such traffic management actions as traffic signal setting, network design, and congestion pricing. The lower-level problem of the MPEC describes ...

By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is O(2nn 5 2 ), we prove that solving this n-dimensional linear optimization problem requires at least 2n − 1 iterations.

The purpose of this paper is to introduce and study Generalized Minty Variational Inequalities in Banach spaces. We consider a problem of vector variational inequalities, referred as Generalized Minty VI(f ′ − , K), in a real Banach space X, where K is a nonempty subset of X and f ′ − is the lower Dini directional derivative of a real function f defined on an open set in X containing K. The res...

In this paper, we consider a vector optimization problem involving locally Lipschitz generalized approximately convex functions and provide several concepts of approximate efficient solutions. We formulate variational inequalities Minty Stampacchia type under the framework Clarke subdifferentials use these as tool to characterize an solution problem.

Linear programming (LP) is an important field of optimization. Even though, interior point methods are polynomial algorithms, many LP practical problems are solved more efficiently by the primal and dual revised simplex methods (RSM); however, RSM has a poor performance in hard LP problems (HLPP) as in the Klee-Minty Cubes problem. Among LP methods, the hybrid method known as Simplex-Genetic (S...