Roman Sznajder

Some Global Uniqueness and Solvability Results for Linear Complementarity Problems Over Symmetric Cones

The purpose of this paper is to give a numerical treatment for a class of quasi-linear elliptic equations under nonlinear boundary conditions, including the three basic types of linear boundary conditions. The quasi-linear equation is discretized by the finite difference method, and the method of upper-lower solutions and its associated monotone iteration are used to compute the solutions of the finite difference system. This method leads to monotone iterative schemes for the computation of numerical solutions as well as some comparison results among the monotone iterative schemes. It also leads to the existence of a maximal and a minimal finite difference solution, including the uniqueness of the solution, and the convergence of the finite difference solution to the corresponding continuous solution. Applications are given to two physical problems in heat conduction and combustion theory, and numerical results for the heat-conduction problem are given, and are compared with the known true continuous solution.

Automorphism Invariance of P- and GUS-Properties of Linear Transformations on Euclidean Jordan Algebras

Generalizing the P-property of a matrix, Gowda et al. [Gowda, M. S., R. Sznajder, J. Tao. 2004. Some P-properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl.393 203232] recently introduced and studied P- and globally uniquely solvable (GUS)-properties for linear transformations defined on Euclidean Jordan algebras. In this paper, we study the invariance of these properties under automorphisms of the algebra and of the symmetric cone. By means of these automorphisms and the concept of a principal subtransformation, we introduce and study ultra and super P-(GUS)-properties for a linear transformation on a Euclidean Jordan algebra.

The Generalized Order Linear Complementarity Problem

The generalized order linear complementarity problem (in the setting of a finite dimensional vector lattice) is the problem of finding a solution to the piecewise-linear system

Generalizations of P0- and P-properties; extended vertical and horizontal linear complementarity problems

x \wedge (M_{1}x + q_{l}) \wedge (M_{2}x + q_{2}) \wedge \cdots \wedge (M_{k}x + q_{k}) = 0,

A generalization of the Nash equilibrium theorem on bimatrix games

where

On the Limiting Behavior of the Trajectory of Regularized Solutions of a P0-Complementarity Problem

M_i

On the Lipschitzian properties of polyhedral multifunctions

s are linear transformations and

More results on Schur complements in Euclidean Jordan algebras

q_i