Annals of Operations Research 47(1993)443--482 443 A simplified global convergence proof of the affine scaling algorithm* R.D.C. Monteiro Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA T. Tsuchiya The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-Ku, Tokyo 106, Japan Y. Wang Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA This paper presents a simplified and self-contained global convergence proof for the affine scaling algorithm applied to degenerate linear programming problems. Convergence of the sequence of dual estimates to the center of the optimal diial face is also proven. In addition, we give a sharp rate of convergence result for the sequence of objective function values. All these results are proved with respect to the long step version of the affine scaling algorithm in which we move a fraction A, where A G {0,2/3], of the step to the boundary of the feasible region. 1. Introduction The affine scaling algorithm, introduced by Dikin [6] in 1967, is one of the simplest and most efficient interior point algorithms for solving linear program- ming (LP) problems. Because of the theoretical and practical importance of the affine scaling algorithm, there are a number of papers which study its global and local convergence [3, 6-8, 11, 16, 19-24] and the behavior of its associated con- tinuous trajectories [2, 4, 16, 25]. As in the simplex algorithm, the analysis of the affine scaling algorithm for (primal) degenerate LP problems is much harder than for (primal) nondegenerate LP problems. *This research was supported by the National Science Foundation (NSF) under Grant No. DDM- 9109404 and the Overseas Research Scholars of the Ministry of Education, Science and Culture of Japan. © J-C. Baltzer AG, Science Publishers