Convergence of the Gradient Sampling Algorithm for Nonsmooth Nonconvex Optimization

Authors:
Krzysztof C. Kiwiel
Affiliations:
-
Venue:
SIAM Journal on Optimization
Year:
2007

Citing 0
Cited 3

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A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization

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Abstract

We study the gradient sampling algorithm of Burke, Lewis, and Overton for minimizing a locally Lipschitz function $f$ on $\mathbb{R}^n$ that is continuously differentiable on an open dense subset. We strengthen the existing convergence results for this algorithm and introduce a slightly revised version for which stronger results are established without requiring compactness of the level sets of $f$. In particular, we show that with probability 1 the revised algorithm either drives the $f$-values to $-\infty$, or each of its cluster points is Clarke stationary for $f$. We also consider a simplified variant in which the differentiability check is skipped and the user can control the number of $f$-evaluations per iteration.