There has been a great deal of success in the last 20 years with the use of cutting plane algorithms to solve specialized integer programming problems. Generally, these algorithms work by solving a sequence of linear programming relaxations of the integer programming problem, and they use the simplex algorithm to solve the relaxations. In this paper, we describe experiments using a predictor-corrector interior point method to solve the relaxations. For some problems, the interior point code requires considerably less time than a simplex based cutting plane algorithm.
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John E. Mitchell (2000) studied this question.
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