Abstract
Abstract An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a seque:1ce of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving integer programming problems is of this form: linear programming relaxations are solved unti eventually the integer programming problem has been solved. Within the last ten years, interior point methods have become accepted as powerful tools for solving linear programming problems. It appears that interior point methods may well solve large linear programs substantially faster than the simplex method. A natural question, therefore, is whether interior point methods can be successfully used to solve integer programming problems. This requires the ability to exploit a warm start.
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