BFGS convergence to nonsmooth minimizers of convex functions

Jiayi Guo; Adrian Lewis

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arXiv · 1703.06690

BFGS convergence to nonsmooth minimizers of convex functions

Jiayi Guo·Adrian Lewis

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Abstract

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions, like the Euclidean norm, that are nonsmooth at the minimizer.

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Jiayi Guo, Adrian Lewis. 2017-03-20. BFGS convergence to nonsmooth minimizers of convex functions. https://arxiv.org/abs/1703.06690

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