Isac and Németh [G. Isac and AB Németh, Projection method, isotone projection cones and
the complementarity problem, J. Math. Anal. App., 153, 258-275 (1990)] proved that solving …

The solution of the complementarity problem defined by a mapping f: Rn→ Rn and a cone
K⊂ Rn consists of finding the fixed points of the operator PK∘(If), where PK is the projection …

In this paper we extend the notion of a Lorentz cone in a Euclidean space as follows: we
divide the index set corresponding to the coordinates of points in two disjoint classes. By …

This paper provides a systematic solvability analysis for (generalized) variational
inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature …

In this paper, we analyze the relationship between projected and (possibly accelerated)
modulus-based matrix splitting methods for linear complementarity problems. In particular …

Solutions of a variational inequality problem defined by a closed and convex set and a
mapping are found by imposing conditions for the monotone convergence with respect to a …

We present a new class of Lipschitz operators on Euclidean lattices that we call lattice
Lipschitz maps, and we prove that the associated McShane and Whitney formulas provide …

By using some lattice-like operations which constitute extensions of ones introduced by MS
Gowda, R. Sznajder and J. Tao for self-dual cones, a new perspective is gained on the …

The main motivation for introducing the notion of isotone projection cones was to solve
nonlinear complementarity problems. The notion of*-isotone projection cones is introduced …

In this paper, we first discuss the geometric properties of the Lorentz cone and the extended
Lorentz cone. The self-duality and orthogonality of the Lorentz cone are obtained in Hilbert …