A real square matrix is said to be a P-matrix if all its principal minors are positive. It is well
known that this property is equivalent to: the nonsign-reversal property based on the …

Based on an inverse function theorem for a system of semismooth equations, this paper
establishes several necessary and sufficient conditions for an isolated solution of a …

This article deals with linear complementarity problems over symmetric cones. Our objective
here is to characterize global uniqueness and solvability properties for linear …

Motivated by the similarities between the properties of Z-matrices on R^ n _+ and Lyapunov
and Stein transformations on the semidefinite cone S^ n_+, we introduce and study Z …

In this article, we introduce the concepts of P and P 0 properties for a nonlinear
transformation defined on a Euclidean Jordan algebra and study existence of solution in the …

We study a smoothing Newton method for solving a nonsmooth matrix equation that
includes semidefinite programming and the semidefinite complementarity problem as …

Using duality, complementarity ideas, and Z-transformations, in this chapter we discuss
equivalent ways of describing the existence of common linear/quadratic Lyapunov functions …

Let L be a linear transformation on a finite dimensional real Hilbert space H and K be a
closed convex cone with dual K∗ in H. The cone spectrum of L relative to K is the set of all …

Motivated by the equivalence of the strict semimonotonicity property of the matrix A and the
uniqueness of the solution to the linear complementarity problem LCP (A, q) for q∈ R+ n, we …

In this paper, we present some novel observations for the semidefinite linear
complementarity problems, abbreviated as SDLCPs. Based on these new results, we …