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
Document Type:Article
Parent Title (English):Mathematical Programming Computation
Volume:11
First Page:421
Last Page:455
Publisher:Springer Berlin Heidelberg
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx]
Year of first publication:2019
Preprint:urn:nbn:de:0297-zib-68152
DOI:https://doi.org/10.1007/s12532-019-00154-6