qpOASES: a parametric active-set algorithm for quadratic programming

• Published in: Mathematical programming computation Vol. 6; no. 4; pp. 327 - 363
• Main Authors: Ferreau, Hans Joachim, Kirches, Christian, Potschka, Andreas, Bock, Hans Georg, Diehl, Moritz
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
• Subjects: Full Length Paper; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Optimization; Theory of Computation; Model predictive control; 90C20 (Quadratic programming); 65K05 (Mathematical programming methods); Active set method; Parametric quadratic programming
• ISSN: 1867-2949; 1867-2957
• DOI: 10.1007/s12532-014-0071-1

Many practical applications lead to optimization problems that can either be stated as quadratic programming (QP) problems or require the solution of QP 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-set method 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 the Maros-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.