In this paper, we discuss the perturbation analysis of extended vertical linear complementarity problem (EVLCP). Under assumption row $${\mathcal {W}}$$ -property, derive several absolute and relative bounds EVLCP, which extend some existing results. Several numerical examples are given to show proposed bounds.

The extended linear complementarity problem (XLCP) has been introduced in a recent paper by Mangasarian and Pang. In the present research, minimization problems with simple bounds associated to this problem are deened. When the XLCP is solvable, their solutions are global minimizers of the associated problems. Suucient conditions that guarantee that stationary points of the associated problems ...

An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if com-plementarity conditions are imposed on input and output variables of linear dynamical in-put/state/output systems. The resulting dynamical systems are called linear complementar-ity systems. Since the RCP is crucial both in issu...

We consider the linear complementarity problem (LCP): Mz + q ≥ 0, z ≥ 0, z′(Mz + q) = 0 as an absolute value equation (AVE): (M + I)z + q = |(M − I)z + q|, where M is an n× n square matrix and I is the identity matrix. We propose a concave minimization algorithm for solving (AVE) that consists of solving a few linear programs, typically two. The algorithm was tested on 500 consecutively generat...

The first algorithm to use a complementary pivoting procedure was that devised by Lemke and Howson to find a Nash equilibrium point of a bimatrix game [ 15 ]. This algorithm introduced a novel proof of convergence not relying on standard monotonicity arguments. Lemke [ 12] generalized his complementary pivot algorithm to solve certain classes of linear complementarity problem (LCP), which Dantz...

The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the GUS property of the linear transformation of the second-order cone linear complementarity problems (SOCLCP) ...

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by simplex{based pivot algorithms are given in terms of complementary bases. A basis identi cation algorithm is a...