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This article studies a combination of the two state-of-the-art algorithms forthe exact solution of linear programs (LPs) over the rational numbers, i.e.,without any roundoff errors or numerical tolerances. By integrating the methodof precision boosting inside an LP iterative refinement loop, the combinedalgorithm is able to leverage the strengths of both methods: the speed of LPiterative refinement, in particular in the majority of cases when adouble-precision floating-point solver is able to compute approximate solutionswith small errors, and the robustness of precision boosting whenever extendedlevels of precision become necessary. We compare the practical performance ofthe resulting algorithm with both puremethods on a large set of LPs andmixed-integer programs (MIPs). The results show that the combined algorithmsolves more instances than a pure LP iterative refinement approach, while beingfaster than pure precision boosting. When embedded in an exact branch-and-cutframework for MIPs, the combined algorithm is able to reduce the number offailed calls to the exact LP solver to zero, while maintaining the speed of thepure LP iterative refinement approach.

Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization