It has been shown by Lemke that if a matrix is copositive plus on IR n , then feasibility of the corresponding Linear Complementarity Problem implies solvability. In this article we show, under suitable conditions, that feasibility of a Generalized Linear Complementarity Problem (i.e., deened over a more general closed convex cone in a real Hilbert Space) implies solvability whenever the operat...

The linear complementarity problem (q,A) with data A ∈ Rn×n and q ∈ Rn involves finding a nonnegative z ∈ Rn such that Az+ q ≥ 0 and zt(Az+ q) = 0. Cottle and Stone introduced the class of P1-matrices and showed that if A is in P1\Q, then K(A) (the set of all q for which (q,A) has a solution) is a half-space and (q,A) has a unique solution for every q in the interior of K(A). Extending the resu...

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...

or to conclude that no such vectors ω, z exist. The inequalities appearing in (1) and in the sequel are understood componentwise and o denotes the zero vector. Many applications and solution methods for (1) can be found in [3] and [4], respectively. In [8] (see also Section 9.2 in [4]), the so-called modulus algorithm was developed for solving the LCP: Let I denote the identity and with x ∈ R w...

In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonst...

We present a method for smoothing discontinuous dynamics involving contact and friction, thereby facilitating the use of local optimization techniques for control. The method replaces the standard Linear Complementarity Problem with a Stochastic Linear Complementarity Problem. The resulting dynamics are continuously differentiable, and the resulting controllers are robust to disturbances. We de...

Motivated by a recent (continuous) quadratic formulation, in this paper we present a pivoting-based heuristic for graph matching based on the corresponding linear complementarity problem. Experiments are presented which demonstrate the potential of the proposed method. 2002 Elsevier Science B.V. All rights reserved.

The paper generalizes the Mangasarian-Ren 10] error bounds for linear complementarity problems (LCPs) to nonlinear complementarity problems (NCPs). This is done by extending the concept of R 0-matrix to several R 0-type functions, which include a subset of monotone functions as a special case. Both local and global error bounds are obtained for the R 0-type and some monotone NCPs.

We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our returns primal-dual optimal when available or certificates of infeasibility otherwise. It is derived by applying Douglas--Rachford splitting homogeneous embedding the linear complementarity problem, which general set membership includes prog...