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BFGS convergence to nonsmooth minimizers of convex functions

Jiayi Guo(jg826***at***cornell.edu)
Adrian Lewis(adrian.lewis***at***cornell.edu)

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.

Keywords: convex; BFGS; quasi-Newton; nonsmooth

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Manuscript: School of ORIE, Cornell University.

Download: [PDF]

Entry Submitted: 03/19/2017
Entry Accepted: 03/19/2017
Entry Last Modified: 03/19/2017

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