Certifying and repairing solutions to large LPs how good are LP-solvers?

摘要

State-of-the-art linear programming (LP) solvers give solutions without any warranty. Solutions are not guaranteed to be optimal or even close to optimal. Of course, it is generally believed that the solvers produce optimal or at least close to optimal solutions.We have implemented a system LPex which allows us to check this belief. More precisely, given an LP and a basis B, it determines whether the basis is primal feasible and/or dual feasible. It can also find the optimum starting from an arbitrary basis (or from scratch). It uses exact arithmetic to guarantee correctness of the results. The system is efficient enough to be applied to medium- to large-scale LPs. We present results from the netlib benchmark suite.