Principal pivoting method for solving column sufficient complementarity problems

The linear complementarity problem (q, A) is to nd, for a given real square matrix A of order n and a real column vector q of order n, a nonnegative v ector z such that Az + q greater than or equal to 0 and z(t) (Az + q) = 0. It is known that when A is a positive semidefinite matrix, one can use a pr incipal pivoting method to compute a solution to (q, A) if it has one and t o conclude that the problem has no solution otherwise. Cottle, Pang, and Ve nkateswaran [ Linear Algebra Appl., 114/115 (1989), pp. 231-249] introduced the class of sufficient matrices and widened the scope of a principal pivo ting algorithm to solve linear complementarity problems with row sufficient matrices. Our main result in this article is to show that this algorithm c an be extended to solve even the problems with column sufficient matrices.