A quasi-Newton algorithm for nonconvex, nonsmooth optimization with global convergence guarantees

  • A line search algorithm for minimizing nonconvex and/or nonsmooth objective functions is presented. The algorithm is a hybrid between a standard Broyden–Fletcher–Goldfarb–Shanno (BFGS) and an adaptive gradient sampling (GS) method. The BFGS strategy is employed because it typically yields fast convergence to the vicinity of a stationary point, and together with the adaptive GS strategy the algorithm ensures that convergence will continue to such a point. Under suitable assumptions, it is proved that the algorithm converges globally with probability one. The algorithm has been implemented inC++and the results of numerical experiments illustrate the efficacy of the proposed approach.

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Metadaten
Author:Frank E. Curtis, Xiaocun Que
DOI:https://doi.org/10.1007/s12532-015-0086-2
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2015
Tag:Software; Theoretical Computer Science
Volume:7
Issue:4
Page Number:30
First Page:399
Last Page:428
Mathematical Programming Computation :MPC 2015 - Issue 4
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