We consider a variational inequality problem, where the cost mapping is the sum of a single-valued mapping and the subdifferential mapping of a convex function. For this problem we introduce a new class of equivalent optimization formulations; based on them, we also provide the first convergence analysis of descent algorithms for the problem. The optimization formulations constitute generalizat...

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

In this paper we study a variational inequality over a product of sets, governed by a multi-valued mapping, in pseudomonotonicity conditions. We are interested in the existence of the solution and, when the inequality depends on a parameter, also in the behavior of the solution at perturbations of the parameter. Mathematics subject classification (2000): 47J20, 58E35, 49N60.

We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculu...

<p style='text-indent:20px;'>This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, this study, a strong convergence result is obtained without assuming Lipschitz continuity of associated mapping operator norm adaptive. Additio...

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...

<p style='text-indent:20px;'>A new strong convergence iterative method for solving a split variational inclusion problem involving bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an scheme comprised of inertial extrapolation step together with the Mann-type step. A theorem iterates generated by given under suitable conditions. I...

This paper presents novel results about the structure of solutions for certain evolutionary variational inequality problems. We show that existence of piecewise solutions is dependant upon the form of the constraint set underlying the evolutionary variational inequality problem considered. We discuss our results in the context of double-layered dynamics theory and we apply them to the modelling...