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Self-Correcting Variable-Metric Algorithms for Nonsmooth Optimization

Frank E. Curtis (frank.e.curtis***at***gmail.com)
Daniel P. Robinson (daniel.p.robinson***at***gmail.com)
Baoyu Zhou (baz216***at***lehigh.edu)

Abstract: A generic algorithmic framework is proposed for minimizing nonsmooth and potentially nonconvex objective functions. The framework is variable-metric in the sense that, in each iteration, a step is computed using a symmetric positive definite matrix whose value is updated in a similar manner as in the Broyden-Fletcher-Goldfarb-Shanno (BFGS) scheme popular for minimizing smooth objectives. Unlike previously proposed variable-metric algorithms for minimizing nonsmooth functions, the proposed framework exploits the self-correcting properties of BFGS-type updating. In so doing, the framework does not overly restrict the manner in which the step computation matrices are updated, yet the scheme is controlled well enough that global convergence guarantees can be established. The results of numerical experiments for various algorithms are presented to demonstrate the self-correcting behaviors that are guaranteed by the framework.

Keywords: nonlinear optimization, nonsmooth optimization, variable-metric algorithms, quasi-Newton methods, self-correcting properties of BFGS updating

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Nonlinear Optimization

Citation: Lehigh ISE COR@L Technical Report 17T-012

Download: [PDF]

Entry Submitted: 10/18/2017
Entry Accepted: 10/18/2017
Entry Last Modified: 03/15/2018

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