QPALM: A Newton-type Proximal Augmented Lagrangian Method for Quadratic Programs

Abstract

We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case to finding the zero of a one-dimensional monotone, piecewise affine function and can be carried out very efficiently. Our algorithm requires the solution of a linear system at every iteration, but as the matrix to be factorized depends on the active constraints, efficient sparse factorization updates can be employed like in active-set methods. Both primal and dual residuals can be enforced down to strict tolerances and otherwise infeasibility can be detected from intermediate iterates. A C implementation of the proposed algorithm is tested and benchmarked against other state-of-the-art QP solvers for a large variety of problem data and shown to compare favorably against these solvers.