On the Local Convergence Analysis of the Gradient Sampling Method for Finite Max-Functions

Elias Salomão Helou (), Sandra A. Santos () and Lucas E. A. Simões ()
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Elias Salomão Helou: University of São Paulo
Sandra A. Santos: University of Campinas
Lucas E. A. Simões: University of Campinas

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 1, No 7, 137-157

Abstract: Abstract The gradient sampling method is a recently developed tool for solving unconstrained nonsmooth optimization problems. Using just first-order information about the objective function, it generalizes the steepest descent method, one of the most classical methods for minimizing a smooth function. This study aims at determining under which circumstances one can expect the same local convergence result of the Cauchy method for the gradient sampling algorithm under the assumption that the problem is stated by a finite max-function around the optimal point. Additionally, at the end, we show how to practically accomplish the required hypotheses during the execution of the algorithm.

Keywords: Nonsmooth nonconvex optimization; Gradient sampling; Local convergence; Unconstrained minimization; 90C30; 65K05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1160-x

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