In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems,...

Generalized second–order directional derivatives for nonsmooth real–valued functions are studied and their connections with second–order variational sets are investigated. A necessary second–order optimality condition for problems with inequality constraints is obtained.

The multi-leader-follower game can be looked on as a generalization of the Nash equilibrium problem and the Stackelberg game, which contains several leaders and a number of followers. Recently, the multi-leader-follower game has been drawing more and more attention, for example, in electricity power markets. However, when we formulate a general multi-leader-follower game as a single-level game,...

The existence of an equilibrium in an extended Walrasian economic model of exchange is confirmed constructively by an iterative scheme. In this scheme, truncated variational inequality problems are solved in which the agents’ budget constraints are relaxed by a penalty representation. Epi-convergence arguments are employed to show that, in the limit, an equilibrium of the targeted type is obtai...

The existence of an equilibrium in an extended Walrasian economic model of exchange is confirmed constructively, under broad assumptions, by an iterative process. In this process, truncated variational inequality problems are solved in which the agents’ budget constraints are furnished with a penalty representation. Epi-convergence arguments are used to show that, in the limit, an equilibrium o...

This paper addresses Henig efficiency of a multi-product network equilibrium model based on Wardrop’s principle. We show that in both the single and multiple criteria cases, such proper efficiency can be recast as a vector variational inequality. In the multiple criteria case, we derive a sufficient and a necessary condition for Henig efficiency in terms of a vector variational inequality by us...

This paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang, Bai, and Kang, [Comp. Math. Appl., 40, 2000]. The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets.

This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.