We consider a vector variational inequality in a finite-dimensional space. A new gap function is proposed, and an equivalent optimization problem for the vector variational inequality is also provided. Under some suitable conditions, we prove that the gap function is directionally differentiable and that any point satisfying the first-order necessary optimality condition for the equivalent opti...

Solving linear variational inequality by traditional numerical iterative algorithm not only can not satisfy parallel, but also its precision has much relationship with initial values. In this paper, a novel hybrid coevolutionary particle swarm optimization is used to solve linear variational inequality, which sufficiently exerts the advantage of particle swarm optimization such as group search,...

and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as th...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent Newton methods for nonsmooth equations have been well established via the concept of semismoothness. When the constraint set of the variational inequality problem is a rectangle, several locally convergent Newton methods for the reformulated nonsmooth e...

 ‎In this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎Our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for Szulkin-type functionals.

in this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in hilbert spaces.

this paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   the main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

Here, 2 ≤ p < ∞, j : Z × R → R is a function which is measurable in z ∈ Z and locally Lipschitz in x ∈ R and ∂ j(z,x) is the Clarke subdifferential of j(z, ·). If f : Z × R → R is a measurable function which is in general discontinuous in the x ∈ R variable, for almost all z ∈ Z, all M > 0, and all |x| ≤ M, we have | f (z,x)| ≤ aM(z) with aM ∈ L1(Z) and we set j(z,x) = ∫x 0 f (z, r)dr, then j(z...

In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by impulsive differential equation. The existence mild solution for hemivariational inequality is obtained Rothe method, subjectivity multivalued pseudomonotone operators and property derivative. Notice that imply some new fractional viscoelastic constitutive laws.