Since Dantzig's invention of the simplex method, LP algorithms have been improved continuously both in theory and practice to become one of the main workhorses in mathematical optimization and its applications. Most efficient LP solvers today, however, are based on double-precision floating-point arithmetic, which limits their applicability for certain numerically challenging models or applications that require proven exact solutions.

This talk will present the state-of-the art in computing high-precision solutions for linear programs over the rational numbers. We show how an iterative refinement strategy (G., Steffy, Wolter 2012) implemented in the simplex-based LP solver SoPlex can be used to compute accurate solutions without the need for time-consuming pivots or matrix factorizations in exact rational arithmetic. We demonstrate its benefits by numerical results on two applications: the modelling of bacterial growth by flux balance analysis and the design of wireless telecommunication networks.