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A trust-region approach to linearly constrained optimization

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1066))

Abstract

This paper suggests a class of trust-region algorithms for solving linearly constrained optimization problems. The algorithms use a “local” active-set strategy to select the steps they try. This strategy is such that degeneracy and zero Lagrange multipliers do not slow convergence (to a first-order stationary point) and that no anti-zigzagging precautions are necessary. (Unfortunately, when there are zero Lagrange multipliers, convergence to a point failing to satisfy second-order necessary conditions remains possible.) We discuss specialization of the algorithms to the case of simple bounds on the variables and report preliminary computational experience.

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Authors
  1. David M. Gay
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David F. Griffiths

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© 1984 Springer-Verlag

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Gay, D.M. (1984). A trust-region approach to linearly constrained optimization. In: Griffiths, D.F. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099519

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  • DOI: https://doi.org/10.1007/BFb0099519

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13344-5

  • Online ISBN: 978-3-540-38881-4

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