Iterative Refinement for Linear Programming
提出一种迭代精化过程，通过求解一系列精度受限的线性规划问题，计算扩展精度或精确解，适用于需要高精度解的优化场景。
We describe an iterative refinement procedure for computing extended-precision or exact solutions to linear programming (LP) problems. 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, and 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 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.