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Matrix factorizations in optimization of nonlinear functions subject to linear constraints

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Abstract

Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, variable metric, and modified Newton methods.

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Authors and Affiliations

  1. The City College of New York, New York, N.Y., USA

    Donald Goldfarb

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  1. Donald Goldfarb
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Additional information

Part of this work was performed while the author was a visitor at Stanford University. This research was supported in part by the National Science Foundation under Grant GJ 36472 and in part by the Atomic Energy Commission Contract No. AT(04-3)-326PA30.

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Goldfarb, D. Matrix factorizations in optimization of nonlinear functions subject to linear constraints. Mathematical Programming 10, 1–31 (1976). https://doi.org/10.1007/BF01580651

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  • DOI: https://doi.org/10.1007/BF01580651

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