A simplified global convergence proof of the affine scaling algorithm

A simplified global convergence proof of the affine scaling algorithm

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Article ID: iaor19941141
Country: Switzerland
Volume: 46/47
Issue: 1/4
Start Page Number: 443
End Page Number: 482
Publication Date: Dec 1993
Journal: Annals of Operations Research
Authors: , ,
Abstract:

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 dual face is also proven. In addition, the authors 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 they move a fraction λ, where λ∈(0,2/3], of the step to the boundary of the feasible region.

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