A direct search quasi-Newton method for nonsmooth unconstrained optimization

Christopher John Price

Abstract


A direct search quasi-Newton algorithm is presented for local minimization of Lipschitz continuous black-box functions. The method estimates the gradient via central differences using a maximal frame around each iterate. When nonsmoothness prevents progress, a global direction search is used to locate a descent direction. Almost sure convergence to Clarke stationary point(s) is shown, where convergence is independent of the accuracy of the gradient estimates. Numerical results show that the method is effective in practice.


doi:10.1017/S1446181117000323

Keywords


derivative free, nonconvex, Clarke generalized derivative.



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.10651



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.