Minimum norm solution to the positive semidefinite linear complementarity problem

Abstract

In this article, we present an algorithm to compute the minimum norm solution of the positive semidefinite linear complementarity problem. We show that its solution can be obtained using the alternative theorems and a convenient characterization of the solution set of a convex quadratic programming problem. This problem reduces to an unconstrained minimization problem with once differentiable convex objective function. We propose an extension of Newton's method for solving the unconstrained optimization problem. Computational results show that convergence to high accuracy often occurs in just a few iterations.

Keywords:

• alternative theorems
• linear complementarity problem
• minimum norm solution
• solution set of convex problem

AMS Subject Classifications::

• 90C05
• 90C51