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Approximations to the Clarke Generalized Jacobians and Nonsmooth Least-Squares Minimization

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Progress in Optimization

Part of the book series: Applied Optimization ((APOP,volume 30))

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Abstract

Here we use a uniform approximation to the Clarke generalized Jacobian to design an algorithm for solving a class of nonsmooth least-squares minimization problems: \(\min \phi (x) \equiv \frac{1}{2}\sum\nolimits_{i = 1}^m {{f_i}{{(x)}^2} \equiv \frac{1}{2}F{{(x)}^T}F(x),} \) where F : ℝn → ℝm is a locally Lipschitz mapping. We approximate the Clarke subdifferential of φ by approximating the Clarke generalized Jacobian of F. Regularity conditions for global convergence are discussed in details.

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Authors and Affiliations

  1. School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Vic., 3353, Australia

    H. Xu, A. M. Rubinov & B. M. Glover

Authors
  1. H. Xu
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  2. A. M. Rubinov
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  3. B. M. Glover
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© 1999 Kluwer Academic Publishers

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Xu, H., Rubinov, A.M., Glover, B.M. (1999). Approximations to the Clarke Generalized Jacobians and Nonsmooth Least-Squares Minimization. In: Progress in Optimization. Applied Optimization, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3285-5_10

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  • DOI: https://doi.org/10.1007/978-1-4613-3285-5_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3287-9

  • Online ISBN: 978-1-4613-3285-5

  • eBook Packages: Springer Book Archive

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