Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained di erentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the ...

In this work, we consider a generalized nonlinear variational-like inequality problem in the setting of locally convex topological vector spaces and prove the existence of its solutions. © 2005 Published by Elsevier Ltd MSC: 49J40; 47H19; 47H10

We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through ...

I) We consider a system governed by a free boundary problem with Tresca condition on a part of the boundary of a material domain with a source term g through a parabolic variational inequality of the second kind. We prove the existence and uniqueness results to a family of distributed optimal control problems over g for each parameter h > 0, associated to the Newton law (Robin boundary conditio...

Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.

First, this paper introduces a notion of a sharp penalty mapping which can replace more common exact penalty function for convex feasibility problems. Second, it uses it for solution of variational inequalities with monotone operators or pseudo-varitional inequalities with oriented operators. Appropriately scaled the sharp penalty mapping can be used as an exact penalty in variational inequalit...

We propose easily implementable algorithms for minimizing the norm with pseudomonotone variational inequality constraints. This bilevel problem arises in the Tikhonov regularization method for pseudomonone variational inequalities. Since the solution set of the lower variational inequality is not given explicitly, the available methods of mathematical programming and variational inequality can ...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent nonsmooth Newton methods for nonsmooth equations have been well established via the concept of semismoothness. In this paper, we focus our discussions on a way of globalizing nonsmooth Newton methods based on a smoothing-nonsmooth reformulation of nonsm...