More on positive subdefinite matrices and the linear complementarity problem

In this article, we consider positive subdefinite matrices (PSBD) recently studied by J-P. Crouzeix et al. [SIAM J. Matrix Anal. Appl. 22 (2000) 66] a nd show that linear complementarity problems with PSBD matrices of rank gre ater than or equal to 2 are processable by Lemke's algorithm and that a PSB D matrix of rank greater than or equal to 2 belongs to the class of suffici ent matrices introduced by R.W. Cottle et al. [Linear Algebra Appl. 114/115 (1989) 231]. We also show that if a matrix A is a sum of a merely positive subdefinite copositive plus matrix and a copositive matrix, and a feasibil ity condition is satisfied, then Lemke's algorithm solves LCP(q, A). This s upplements the results of Jones and Evers. (C) 2001 Elsevier Science Inc. A ll rights reserved.