‎financial market modeling and prediction is a difficult problem and drastic changes of the price causes nonlinear dynamic that makes the price prediction one of the most challenging tasks for economists‎. ‎since markets always have been interesting for traders‎, ‎many traders with various beliefs are highly active in a market‎. ‎the competition among two agents of traders‎, ‎namely trend follo...

The equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalization of Nash equilibrium problem (NEP) and the mathematical program with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a special class of EPECs where a common parametric P-matrix linear compl...

This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbe...

The property that a pair of oriented matroidsM ? L , M R on E have free union and no common (non-zero) covector generalizes oriented matroid duality. This property characterizes when certain systems of equations whose only nonlinearities occur as real monotone bijections have a unique solution for all values of additive parameters. Instances include sign non-singularity of square matrices and g...

In [8] the notion of “projected differential equation” has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in [20], Minty variational inequalities have been involved in the study of properties of the trajectories of such a projected differential equation. We consider classical generalizations of both problems,...

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

We introduce non-autonomous continuous dynamical systems which are linked to the Newton and Levenberg-Marquardt methods. They aim at solving inclusions governed by maximal monotone operators in Hilbert spaces. Relying on the Minty representation of maximal monotone operators as lipschitzian manifolds, we show that these dynamics can be formulated as first-order in time differential systems, whi...