We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine Hadamard manifolds.

‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property ...

In this paper, we present the concept of generalized invexity for vector-valued functions. Also, we consider different kinds of generalized vector variational-like inequality and a vector optimization problem. Some relations between vector variational-like inequalities and a vector optimization problem are established by using the properties of Mordukhovich limiting subdifferential. Acknowledge...

We consider vector variational inequalities defined by means of the usual componentwise ordering in a finite dimensional Euclidean space. Our principal result shows that, under suitable convexity assumptions, every weak solution of a vector variational inequality is a strong solution of a reduced variational inequality, obtained from the initial one by considering a selection of components.

——————————————————————————————– Abstract: In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide...

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 ...

In this paper, we consider and study a class of vector variational-like inequalities in Banach space without any generalized monotonicity by exploiting vector version of minimax inequality and obtain the existence results of solutions to the class of vector variational-like inequalities. The results presented here are different from [1, 5, 11], and extend and generalize the corresponding result...

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...