we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...

We establish two global bounds measuring the distance from any vector to the solution set of the co-coercive variational inequality. To prove our results, we use the fact that the co-coercivity condition is sufficient for the (strong) monotonicity of (perturbed) fixed point and normal maps associated with variational inequalities.

In this paper, several classes of vector F -complementarity problems (in short, VF -CP) and vector F -variational inequalities (in short, VF -VI) with relations determined by nonconvex preferences are introduced in Banach spaces. Some characterizations of solution sets for (VF -CP) and (VF -VI) are also presented. Furthermore, the results obtained are applied to vector optimization problems.

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems are established

In this paper, we introduce a system of vector equilibrium problems and prove the existence of a solution. As an application, we derive some existence results for the system of vector variational inequalities. We also establish some existence results for the system of vector optimization problems, which includes the Nash equilibrium problem as a special case.

Abstract: In this work, a nonsmooth multiobjective optimization problem involving generalized invexity with cone constraints and Applications (for short, (MOP)) is considered. The Kuhn-Tucker necessary and sufficient conditions for (MOP) are established by using a generalized alternative theorem of Craven and Yang. The relationship between weakly efficient solutions of (MOP) and vector valued s...

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...