Pattern Search Method for Discrete L 1–Approximation

  • C. Bogani
  • M. G. Gasparo
  • A. Papini


We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging.


Pattern search methods Nonsmooth optimization Linear L1–estimation Convex optimization 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Ulisse Dini”Università di FirenzeFirenzeItaly
  2. 2.Dipartimento di Energetica “Sergio Stecco”Università di FirenzeFirenzeItaly

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