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Trust region algorithms for the nonlinear least distance problem

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Abstract

The nonlinear least distance problem is a special case of equality constrained optimization. Let a curve or surface be given in implicit form via the equationf(x)=0,x ∈R d, and letz ∈R d be a fixed data point. We discuss two algorithms for solving the following problem:Find a point x * such that f(x * )=0and ∥z−x *∥2 is minimal among all such x. The algorithms presented use thetrust region approach in which, at each iteration, an, approximation to the objective function or merit function is minimized in a given neighborhood (the trust region) of the current iterate. Among other things, this allows one to prove global convergence of the algorithm.

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Authors and Affiliations

  1. Mathematisches Seminar der Landwirtschaftlichen Fakultät, Universität Bonn, Bonn, Germany

    H. -P. Helfrich

  2. Department of Mathematics and Statistics, University of Vermont, 05401, Burlington, VT, USA

    D. Zwick

Authors
  1. H. -P. Helfrich
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  2. D. Zwick
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Additional information

Both authors were supported in part by the Deutsche Forschungsgemeinschaft, SFB 350.

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Helfrich, H.P., Zwick, D. Trust region algorithms for the nonlinear least distance problem. Numer Algor 9, 171–179 (1995). https://doi.org/10.1007/BF02143933

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