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Solving Quadratic Programs to High Precision using Scaled Iterative Refinement

Tobias Weber (tobias. weber***at***ovgu.de)
Sebastian Sager (sager***at***ovgu.de)
Ambros Gleixner (gleixner***at***zib.de)

Abstract: 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.

Keywords: Quadratic Programming, Iterative Refinement, Active Set, Rational Calculations

Category 1: Nonlinear Optimization (Quadratic Programming )

Citation: Mathematical Programming Computation, Vol. 11 (3), pp. 421--455, 2019. DOI 10.1007/s12532-019-00154-6 Article link https://link.springer.com/article/10.1007%2Fs12532-019-00154-6

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Entry Submitted: 03/19/2018
Entry Accepted: 03/19/2018
Entry Last Modified: 11/10/2020

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