Self-Scaling Variable Metric (SSVM) Algorithms

Shmuel S. Oren and David G. Luenberger
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Shmuel S. Oren: Xerox Corporation, Palo Alto, California and Stanford University
David G. Luenberger: Stanford University

Management Science, 1974, vol. 20, issue 5, 845-862

Abstract: A new criterion is introduced for comparing the convergence properties of variable metric algorithms, focusing on stepwise descent properties. This criterion is a bound on the rate of decrease in the function value at each iterative step (single-step convergence rate). Using this criterion as a basis for algorithm development leads to the introduction of variable coefficients to rescale the objective function at each iteration, and, correspondingly, to a new class of variable metric algorithms. Effective scaling can be implemented by restricting the parameters in a two-parameter family of variable metric algorithms. Conditions are derived for these parameters that guarantee monotonic improvement in the single-step convergence rate. These conditions are obtained by analyzing the eigenvalue structure of the associated inverse Hessian approximations.

Date: 1974
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:20:y:1974:i:5:p:845-862

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