# Interior-point methods

**DOI:**https://doi.org/10.1007/1-4020-0611-X_475

## INTRODUCTION

Notwithstanding the success of the simplex method for linear programming (LP), there was, even from the earliest days of operations research, a desire to create an algorithm for solving linear programming problems that proceeded on a path through the polytope rather than around its perimeter. Indeed, methods were considered, but until recently, none was as effective as the simplex method. In this article, the motivation for desiring an “interior” path, the concept of the complexity of solving a linear programming problem, a brief his-tory of the developments in the area, and the status of the subject as of this writing are discussed. More complete surveys are given in Gonzaga (1991a, 1991b, 1992), Goldfarb and Todd (1989), Roos and Terlaky (1997), Roos, Terlaky and Vial (1997), Terlaky (1996), Ye (1997), Wright (1996) and Wright (1998). Generalizations to nonlinear problems are briefly discussed as well. For a thorough treatment of interior-point algorithms on those...

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