This paper considers the characterization and computation of sparse solutions and leastp-norm (0 < p < 1) solutions of the linear complementarity problems LCP(q,M). We show that the number of non-zero entries of any least-p-norm solution of the LCP(q,M) is less than or equal to the rank of M for any arbitrary matrix M and any number p ∈ (0, 1), and there is p̄ ∈ (0, 1) such that all least-p-norm...

Motivated by the definition of P†-matrix ([9]), another generalization of a P -matrix for square singular matrices called PD-matrix is proposed first. Then the uniqueness of solution of Linear Complementarity Problems for square singular matrices is proved using PD-matrices. Finally some results which are true for P -matrices are extended to PD-matrices.

We show that the Extended Linear Complementarity Problem (ELCP) can be recast as a standard Linear Complementarity Problem (LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since many extensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP as well. Our equivalence proof is constructive and leads to t...

Where, T z denotes the transpose of the vector z . Many problems in operations research, management science, various scientific computing and engineering areas can lead to the solution of an LCP of the form (1.1). For more details (see, [1,2,3] and the references therein). The early motivation for studying the LCP (M, q) was because the KKT optimality conditions for linear and quadratic program...

We characterize the class of integral square matrices M having the property that for every integral vector q the linear complementarity problem with data M; q has only integral basic solutions. These matrices, called principally unimodular matrices, are those for which every principal nonsingular submatrix is unimodular. As a consequence , we show that if M is rank-symmetric and principally uni...

This paper generalizes the answers that were given by R.W. Cottle to questions that were originally raised by G. Maier. Essentially, we give necessary and sufficient conditions for some notions of monotonicity of solutions for the parametric linear complementarity problem. Our proofs are direct ones and not algorithmic, as Cottle's proofs are, and also cover a broader class of matrices.

Exploring Complexity of Large Update Interior-Point Methods for ) k ( P* Linear Complementarity Problems Based on Kernel Function KEYVAN AMINI* M.REZA PEYGHAMI +,2 ∗ Department of Sciences, Razi University, Kermanshah, Iran + Department of Sciences, Khajeh Nasir Toosi (KNT) University of Technology, Tehran, Iran Abstract. Interior Point Methods not only are the most effective methods in practic...