Computing an Exact Solution in Interior-Point Methods for Linear Programming

Pamela J. Williams, Amr S. El-Bakry, and Richard A. Tapia

To compute an exact solution of a linear program with an interior-point algorithm, finite termination procedures must be added to the algorithmic framework. In a finite number of steps, finite termination procedures advance from an interior-point iterate which is sufficiently close to the solution set to a point on the optimal face. A finite termination procedure consists of a mathematical model to compute an exact solution and indicators to identify the active set of a linear program. In this paper we present a survey of optimal face identification models and solution techniques, introduce a new indicator to identify the active set of a linear program in primal-dual interior-point methods and provide some insight on how to construct a numerically efficient finite termination procedure.

Contact: pwillia@sandia.gov