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

Ben Hermans, Andreas Themelis, Panagiotis Patrinos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4325-4330
Number of pages6
ISBN (Electronic)9781728113982
DOIs
Publication statusPublished - Dec 2019
Externally publishedYes
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
Country/TerritoryFrance
CityNice
Period12/11/1912/13/19

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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