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Generating set search methods for piecewise smooth problems. (English) Zbl 1187.65061
The authors 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. By exploiting the structure of the piecewise smooth optimization problem here the authors are able to avoid the assumption of strict differentiability at a Clarke stationary point , and devise a different essential property of the functions to which the presented algorithms can be successfully applied. Some numerical results are presented to validate the approach.

65K05 Numerical mathematical programming methods
90C56 Derivative-free methods and methods using generalized derivatives
90C30 Nonlinear programming
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