This survey article describes in some detail the mathematical and numerical aspects of function imsl_d_sparse_quadratic_prog (sparse_quadratic_prog for short), the sparse convex quadratic programming solver implemented in IMSL C Numerical Library 8.0. The solver uses an infeasible primal-dual interior-point method to find an optimal solution. All primal-dual interior-point methods are essentially variants of Newton’s method that in every iteration step solve a perturbed system of the first-order optimality conditions in order to drive the new iterate closer to the optimum. Today, such methods are widely seen as very efficient means to solve large-scale linear and convex quadratic programming problems fast and accurately.
Tags: IMSL, IMSL C Library, white paper