• Corpus ID: 237571921

On Some Properties of $K$- type Block Matrices in the context of Complementarity Problem

  title={On Some Properties of \$K\$- type Block Matrices in the context of Complementarity Problem},
  author={A. Dutta and A. K. Das},
In this article we introduceK-type block matrices which include two new classes of block matrices namely block triangularK-matrices and hidden block triangular K-matrices. We show that the solution of linear complementarity problem with K-type block matrices can be obtained by solving a linear programming problem. We show that block triangular K-matrices satisfy least element property. We prove that hidden block triangular K-matrices are Q0 and processable by Lemke’s algorithm. The purpose of… 
Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the Linear Complementarity Problem. Earlier


More on hidden Z-matrices and linear complementarity problem
ABSTRACT In this article, we study linear complementarity problem with hidden Z-matrix. We extend the results of Fiedler and Pták for the linear system in complementarity problem using game theoretic
Properties of some matrix classes based on principal pivot transform
  • A. K. Das
  • Mathematics, Computer Science
    Ann. Oper. Res.
  • 2016
It is shown that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with $$Q_{0}$$Q0-property is captured by sufficient matrices introduced by Cottle et al.
On hidden Z-matrix and interior point algorithm
We propose an interior point method to compute solution of linear complementarity problem LCP (q, A) given that A is a real square hidden Z-matrix (generalization of Z-matrix) and q is a real vector.
On almost type classes of matrices with Q-property
In this article, we introduce a new matrix class almost (a subclass of almost N 0-matrices which are obtained as a limit of a sequence of almost N-matrices) and obtain a sufficient condition for this
Linear complementarity problems solvable by A single linear program
It is shown that the linear complementarity problem of finding az inRn such thatMz + q ⩾ 0, z ⩾ 0 andzT(Mz + q) = 0 can be solved by a single linear program in some important special cases including
On weak generalized positive subdefinite matrices and the linear complementarity problem
In this article, we present a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlósi [J.P. Crouzeix and S. Komlósi, The Linear Complementarity
Some Properties of Generalized Positive Subdefinite Matrices
It is shown that for a subclass of GPSBD matrices, the solution set of a linear complementarity problem is same as the set of Karush--Kuhn--Tucker-stationary points of the corresponding quadratic programming problem.
Hidden Z-matrices with positive principal minors☆
Abstract Let C denote the class of hidden Z-matrices, i.e., M∈ C if and only if there exist Z-matrices X and Y such that the following two conditions are satisfied: ( M 1) MX = Y, ( M 2) r T X + s T
Linear complementarity problems solvable by a polynomially bounded pivoting algorithm
A sufficient condition is given under which the parametric principal pivoting algorithm will compute the unique solution to a linear complementarity problem defined by an n by n P-matrix in no more
A note on linear complementarity problems and multiple objective programming
It is felt that solving any LCP by the approach given in [3] may not be as useful as it is claimed.