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Pattern Search Method for Discrete L_1 - Approximation

Claudio Bogani (claudio.bogani***at***math.unifi.it)
Maria Grazia Gasparo (mgasparo***at***unifi.it)
Alessandra Papini (alessandra.papini***at***unifi.it)

Abstract: 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.

Keywords: Pattern search methods, Nonsmooth optimization, Convex optimization

Category 1: Convex and Nonsmooth Optimization

Citation: JOTA, (2007) Digital Object Identifier (DOI) 10.1007/s10957-007-9204-2

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Entry Submitted: 12/06/2004
Entry Accepted: 12/06/2004
Entry Last Modified: 06/01/2007

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