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Generating set search methods for piecewise smooth problems

Claudio Bogani (boganic***at***maths.bham.ac.uk)
Mariagrazia Gasparo (mgasparo***at***unifi.it)
Alessandra Papini (apapini***at***unifi.it)

Abstract: We consider a direct search approach for solving nonsmooth minimization problems where the objective function is locally Lipschitz continuous and piecewise continuously differentiable on a finite family of polyhedra. A generating set search method is proposed, which is named "structured" because the structure of the set of nondifferentiability near the current iterate is exploited to define the search directions at each iteration. Some numerical results are presented to validate the approach.

Keywords: Direct search, generating set search, nonsmooth optimization, Clarke's differential calculus

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: SIAM J. Optim., Vol. 20, No. 1, pp. 321-335, 2009. doi: 10.1137/070708032

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Entry Submitted: 11/19/2007
Entry Accepted: 11/20/2007
Entry Last Modified: 04/27/2009

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