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Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization

Abstract:

We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of [15, 19]. To this aim, we consider a new general class of inexact second-order algorithms for unconstrained optimization that includes regularization and trust-region variations of Newton’s method as well as of their linesearch variants. For each method in this class and arbitrary a...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Balliol College
Gould, NIM More by this author
Publisher:
World Scientific Publisher's website
Volume:
7
Pages:
3697-3740
Publication date:
2018-05-03
Acceptance date:
2018-03-15
Pubs id:
pubs:834369
URN:
uri:f9833c0f-880a-4db2-80bc-ed8ec1b906fd
UUID:
uuid:f9833c0f-880a-4db2-80bc-ed8ec1b906fd
Local pid:
pubs:834369
ISBN:
978-981-3272-87-3

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