A Preconditioned Conjugate Gradient Approach to Linear Equality Constrained Minimization

Abstract

We propose a new framework for the application of preconditioned conjugate gradients in the solution of large-scale linear equality constrained minimization problems. This framework allows for the exploitation of structure and sparsity in the context of solving the reduced Newton system (despite the fact that the reduced system may be dense). Numerical experiments performed on a variety of test problems from the Netlib LP collection indicate computational promise.