6814
2019
eng
421
455
11
article
Springer Berlin Heidelberg
0
2019-02-06
--
--
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.
Mathematical Programming Computation
10.1007/s12532-019-00154-6
yes
urn:nbn:de:0297-zib-68152
2018-12-22
Tobias Weber
Ambros Gleixner
Sebastian Sager
Ambros Gleixner
Mathematical programming [See also 49Mxx, 65Kxx]
Mathematical Optimization
Mathematical Optimization Methods
Gleixner, Ambros
MIP-ZIBOPT
MODAL-SynLab
Siemens
MODAL-Gesamt