Solving quadratic programs to high precision using scaled iterative refinement

  • Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and Mészáros benchmark library.

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Metadaten
Author:Tobias Weber, Sebastian Sager, Ambros GleixnerORCiD
DOI:https://doi.org/10.1007/s12532-019-00154-6
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2019
Tag:Software; Theoretical Computer Science
Volume:11
Issue:3
Page Number:35
First Page:421
Last Page:455
Mathematical Programming Computation :MPC 2019 - Issue 3
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