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Pattern search method for discrete \(L_{1}\)-approximation. (English) Zbl 1129.49043
Summary: 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.

49N90 Applications of optimal control and differential games
68T10 Pattern recognition, speech recognition
90C30 Nonlinear programming
90C25 Convex programming
Full Text: DOI
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