A Globally and Superlinearly Convergent Algorithm for Convex Quadratic Programs with Simple Bounds

Abstract

We present a globally and superlinearly convergent algorithm for solving convex quadratic programs with simple bounds. We develop our algorithm using a new formulation of the problem: the minimization of an unconstrained piecewise quadratic function that has the same optimality conditions as the original problem. The major work at each iteration is the Cholesky factorization of a positive definite matrix with the size and structure of the Hessian of the quadratic. Hence our algorithm is suitable for solving large sparse problems and for implementation on parallel computers. We implemented our algorithm and tested it on a sequential computer on a variety of dense problems, and we present numerical results which show that our algorithm solves many problems quickly. Keywords: quadratic programming, interior point methods, simple bounds, box constraints, large sparse minimization.