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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(More)
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(More)
We present an exact rational solver for mixed-integer linear programming which avoids the numerical inaccuracies inherent in the floating-point computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where correct solutions are critical due to legal and financial(More)
We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our(More)
This paper studies K-sublinear inequalities, a class of inequalities with strong relations to K-minimal inequalities for disjunctive conic sets. We establish a stronger result on the suffi-ciency of K-sublinear inequalities. That is, we show that when K is the nonnegative orthant or the second-order cone, K-sublinear inequalities together with the original(More)