Reliable Solution of Convex Quadratic Programs with Parametric Active Set Methods

Parametric Active Set Methods (PASM) are a relatively new class of methods to solve convex Quadratic Programming (QP) problems. They are based on tracing the solution along a linear homotopy between a QP with known solution and the QP to be solved. We explicitly identify numerical challenges in PASM and develop strategies to meet these challenges. To demonstrate the reliability improvements of the proposed strategies we have implemented a prototype code called rpasm. We compare the results of the code with those of other popular academic and commercial QP solvers on problems of a subset of the Maros-Mészáros test examples. Our code is the only one to solve all of the problems with the default settings. Furthermore, we propose how PASM can be used to compute local solutions of nonconvex QPs.