On a primal-dual Newton proximal method for convex quadratic programs

Abstract This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm damped semismooth Newton method. The outer regularization yields numerically stable method, we interpret operator as unconstrained minimization of augmented Lagrangian function. allows inner scheme to exploit sparse symmetric linear solvers multi-rank factorization updates. Moreover, systems are always solvable independently from problem data exact linesearch can be performed. proposed handle degenerate problems, provides mechanism infeasibility detection, warm starting, while requiring only convexity. We present details our open-source C implementation report on numerical results against state-of-the-art solvers. QPDO proves simple, robust, efficient programming.