TY - JOUR
A1 - Gleixner, Ambros
A1 - Steffy, Daniel
A1 - Wolter, Kati
T1 - Iterative Refinement for Linear Programming
T2 - INFORMS Journal on Computing
N2 - 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 show that this algorithm is effective in practice for computing extended precision solutions and that it leads to a direct improvement of the best known methods for solving LPs exactly over the rational numbers. Our implementation is publically available as an extension of the academic LP solver SoPlex.
Y1 - 2016
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/5889
VL - 28
IS - 3
SP - 449
EP - 464
ER -