Commentary—Major Cholesky Would Feel Proud

Probably more than any other group, authors Lustig, Marsten, and Shanno have led the way in demonstrating the effectiveness of interior methods for solving large, real-world linear programs. For several years they have written at length about things they have actually done. There are no pies in the sky, no secrets. They have explored a multitude of algorithmic ideas and implementation strategies, and they have done more than could be asked to share their experience with the rest of the world.

Here, the authors look back on a decade's events that revived barrier methods for constrained optimization and eventually led to their production LP solver OB1. The results reported are indeed impressive. In this commentary, we focus mostly on the “engine”—the Cholesky factorizer—that has made OB1 such a practical success.

INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.