In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is showed that a real symmetric tensor is a (strictly) semi-positi...

We generalize the P, P0, R0 properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of generalized nonlinear complementarity problem (GNCP). We prove that if a continuous function has the order P0 and R0 properties then all the associated GNCPs have solutions.

Most known continuation methods for P0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and the properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose a new homotopy formulation for the complementarity problem based on which a new homotopy conti...

We consider a polyhedron intersected by a two-term disjunction, and we characterize the polyhedron resulting from taking its closed convex hull. This generalizes an earlier result of Conforti, Wolsey and Zambelli on split disjunctions. We also recover as a special case the valid inequalities derived by Judice, Sherali, Ribeiro and Faustino for linear complementarity problems.

We define a new fundamental constant associated with a P-matrix and show that this constant has various useful properties for the P-matrix linear complementarity problems (LCP). In particular, this constant is sharper than the Mathias-Pang constant in deriving perturbation bounds for the P-matrix LCP. Moreover, this new constant defines a measure of sensitivity of the solution of the P-matrix L...

New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a "best" error bound emerges from our comparisons as the sum of two natural residuals.

The paper establishes a computational encIosure of the solution of the linear complementarity problem (q, M), where M is assumed to be an H-matrix with a positive main diagonal. A dass of problems with interval data, which can arise in approximating the solutions of free boundary problems, is also treated successfully.

Although the general linear complementarity problem (LCP) is NP-complete, there are special classes that can be solved in polynomial time. One example is the type where the defining matrix is nondegenerate and for which the n-step property holds. In this paper we consider an extension of the property to the degenerate case by introducing the concept of an extended n-step vector and matrix. It i...

The Q-property of a multiplicative transformation AXAT in semidefinite linear complementarity problems is characterized when A is normal.

This research studies information technology (IT) business value by examining complementarity effects between organizational culture and dynamic IT capability on firm performance. Using the Competing Values Framework, we study the external/internal focus and flexibility/stability dimensions of organizational culture. Here dynamic IT capability refers to the ability to integrate, build, and reco...