In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient ...

This article proposes a new extragradient solution method for strongly pseudomonotone variational inequalities. A detailed analysis of the iterative sequences' convergence and of the range of applicability of the method ...

A variational inequality problem (VIP) satisfying a constraint qualification can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing ...

In this paper we consider the following nonlocal fractional variational inequality u∈X0 s(Ω),u⩽ψa.e. in Ω,〈u,v−u〉X0 s(Ω)−λ〈u,v−u〉2⩾∫Ωfx,u(x),(−Δ)βu(x)(v(x)−u(x))dxaaaaaaaaaaaaaaaaaaaaaaaaaaaaafor anyv∈X0 s(Ω),v⩽ψa.e. in ...

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems ...

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems ...

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple ...