QHOPDM

QHOPDM -- a higher order primal-dual method for large scale convex quadratic programming In 1992 we prepared HOPDM -- a modularly structured library of FORTRAN subroutines for large scale linear optimization. We broadened this software subsequently to use it for a quadratic programming problem generated by a cost-effective sulphur emission reduction model. Success with a real-life model induced us to prepare a more general quadrature solver. We then extended our LP procedure to the case of convex quadratic objectives.par Now we are presenting QHOPDM, a library for convex quadratic optimization with linear constraints. Formally, we solve a problem of the form: minimize $c^Tx+{1over 2} x^TQx$, subject to $Ax= b$, $lle xle h$, where $Q$ is a positive semidefinite matrix and we know any factorization of the form $Q= F^TF$.par Our package QHOPDM is based on the higher primal-dual method of Mehrotra for LP problems and modified by us for QP problems. We stress once more that the quadratic part of the objective (matrix $Q$) must be given in a special form. We assume that a factorization $Q= F^TF$ is known. Knowing such a factorization we can easily construct a separable equivalent problem, which is easy to solve numerically.