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arXiv · 1910.11199

A nonsmooth nonconvex descent algorithm

Jan Mankau·Friedemann Schuricht
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Abstract

The paper presents a new descent algorithm for locally Lipschitz continuous functions $f:X\to\mathbb{R}$. The selection of a descent direction at some iteration point $x$ combines an approximation of the set-valued gradient of $f$ on a suitable neighborhood of $x$ (recently introduced by Mankau & Schuricht) with an Armijo type step control. The algorithm is analytically justified and it is shown that accumulation points of iteration points are critical points of $f$. Finally the algorithm is tested for numerous benchmark problems and the results are compared with simulations found in the literature.

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Jan Mankau, Friedemann Schuricht. 2019-10-24. A nonsmooth nonconvex descent algorithm. https://arxiv.org/abs/1910.11199

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