Mathematical Programming Computation, Volume 6, Issue 4, December 2014

qpOASES: a parametric active-set algorithm for quadratic programming

Hans Joachim Ferreau, Christian Kirches, Andreas Potschka, Hans Georg Bock, Moritz Diehl

Many practical applications lead to optimization problems that can either be stated as quadratic programming (QP) problems or require the solution ofQP problems on a lower algorithmic level. One relatively recent approach to solve QP problems are parametric active-set methods that are based on tracing the solution along a linear homotopy between a QP problem with known solution and the QP problem to be solved. This approach seems to make them particularly suited for applications where a-priori information can be used to speed-up the QP solution or where high solution accuracy is required. In this paper we describe the open-source C++ software package qpOASES,which implements a parametric active-setmethod in a reliable and efficient way. Numerical tests show that qpOASES can outperform other popular academic and commercial QP solvers on small- to medium-scale convex test examples of theMaros-Mészáros QP collection. Moreover, various interfaces to third-party software packages make it easy to use, even on embedded computer hardware. Finally, we describe how qpOASES can be used to compute critical points of nonconvex QP problems.

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