TY - GEN
T1 - QPALM
T2 - 58th IEEE Conference on Decision and Control, CDC 2019
AU - Hermans, Ben
AU - Themelis, Andreas
AU - Patrinos, Panagiotis
N1 - Funding Information:
1Ben Hermans is with the Department of Mechanical Engineering, KU Leuven, and DMMS lab, Flanders Make, Leuven, Belgium. His research benefits from KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC), from project G0C4515N of the Research Foundation - Flanders (FWO - Flanders), from Flanders Make ICON: Avoidance of collisions and obstacles in narrow lanes, and from the KU Leuven Research project C14/15/067: B-spline based certificates of positivity with applications in engineering. 2Andreas Themelis and Panagiotis Patrinos are with the Department of Electrical Engineering (ESAT-STADIUS) – KU Leuven, Kasteelpark Aren-berg 10, 3001 Leuven, Belgium. This work was supported by the Research Foundation Flanders (FWO) research projects G086518N and G086318N; Research Council KU Leuven C1 project No. C14/18/068; Fonds de la Recherche Scientifique — FNRS and the Fonds Wetenschappelijk Onder-zoek — Vlaanderen under EOS project no 30468160 (SeLMA).
PY - 2019/12
Y1 - 2019/12
N2 - We present a proximal augmented Lagrangian based solver for general 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.
AB - We present a proximal augmented Lagrangian based solver for general 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.
UR - http://www.scopus.com/inward/record.url?scp=85078567403&partnerID=8YFLogxK
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U2 - 10.1109/CDC40024.2019.9030211
DO - 10.1109/CDC40024.2019.9030211
M3 - Conference contribution
AN - SCOPUS:85078567403
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4325
EP - 4330
BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 11 December 2019 through 13 December 2019
ER -