1545
eng
reportzib
0
2012-05-08
2012-05-08
--
Improving the Accuracy of Linear Programming Solvers with Iterative Refinement
We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, while numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description.
We demonstrate that this algorithm is effective in practice for computing extended precision solutions and that this leads to direct improvement of the best known methods for solving LPs exactly over the rational numbers.
1438-0064
urn:nbn:de:0297-zib-15451
10.1145/2442829.2442858
Appeared in: ISSAC '12 Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation pp. 187-194
Ambros M. Gleixner
Ambros Gleixner
Daniel Steffy
Kati Wolter
ZIB-Report
12-19
eng
uncontrolled
Linear programming
eng
uncontrolled
Iterative refinement
eng
uncontrolled
Exact linear programming
MATHEMATICAL SOFTWARE
Metrics (D.4.8)
Algorithms (F.2.1-2)
Linear programming
Mathematical Optimization
Gleixner, Ambros
Wolter, Kati
MIP-ZIBOPT
Siemens
SPP1307-ExactIP
https://opus4.kobv.de/opus4-zib/files/1545/ZR_12-19.pdf