Semicoercive Variational Inequalities: From Existence to Numerical Solution of Nonmonotone Contact Problems

Abstract

In this paper, we present a novel numerical solution procedure for semicoercive hemivariational inequalities. As a concrete example, we consider a unilateral semicoercive contact problem with nonmonotone friction modeling the deformation of a linear elastic block in a rail, and provide numerical results for benchmark tests.

Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications

“…In particular, (EP) includes also two families of mixed variational inequalities in which we have special interest since applications in several fields of engineering and economics among others (see [1,21,22,31,15,34,38]) can be cast as such. Recall that given an operator T : K → R n and a function ϕ : K → R, the mixed variational inequality (MVI) problem is defined as find x ∈ K : T (x), y − x + ϕ(y) − ϕ(x) ≥ 0, ∀ y ∈ K, (MVI) MVI while the inverse mixed variational inequality (IMVI) problem is defined as find x ∈ K : x, T (y) − T (x) + ϕ(y) − ϕ(x) ≥ 0, ∀ y ∈ K.…”

“…(IMVI) IMVI Both problems are very general formulations, too, and have been intensively studied in the literature (see [1,17,21,22,36,38,51,54] among others) since they encompass variational inequalities and inverse variational inequalities as a special case (when ϕ = 0, see [12,13]); constrained optimization problems (when T = 0) and even the minimization of the sum of two functions (when T is the gradient of a differentiable function defined on K in problem (MVI)). Furthermore, problem (IMVI) generalizes standard mathematical programming problems such as the extended linear-quadratic programming studied in [42] (see [21]).…”