Solving Quadratic Programs to High Precision using Scaled Iterative Refinement [article]

Tobias Weber, Sebastian Sager, Ambros Gleixner
2018 arXiv   pre-print
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
more » ... 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 M\'esz\'aros benchmark library.
arXiv:1803.07178v1 fatcat:bou6l3gtnffzhkt6o7yph4zhia