In this work, we will establish some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces under invexity hypotheses. This paper extends the earlier work of Ruiz-Garzón et al. [G. Ruiz-Garzón, R. OsunaGómez, A. Rufián-Lizana, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004)...

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...

Merit functions utilized to monitor the convergence of sequential quadratic programming (SQP) methods for nonlinear programs and variational inequality problems have in common that they include a penalty function for the explicit constraints, the value of the penalty parameter for which is subject to the requirement of being large enough compared to estimates of the optimal Lagrange multipliers...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

We introduce an iterative method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is th...

The concept of η-invex set is explored and the concept of T-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended to H-spaces and differentiable n-manifolds. The solution of complementarity problem is also studied in the presence of fixed ...

We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the converg...

In this paper, we design a new projection-type alternating direction method which is an attractive method for solving variational inequality problems, and its application range covers linear programming, semidefinite programming etc. In each iteration, it just solves a linear equation and implements three orthogonal projections to closed convex sets. Under the conditions of monotonicity and Lip...