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A concise second-order complexity analysis for unconstrained optimization using high-order regularized models

Abstract:

An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order p, p≥2, of the unconstrained objective function, and that is guaranteed to find a first- and second-order critical point in at most O(max{ϵ−p+1p1,ϵ−p+1p−12}) function and derivatives evaluations, where ϵ1 and ϵ2 are prescribed first- and second-order optimality tolerances. This is a simple algorithm and associated analysis compared to the much more general approach in Cartis et al. [Sharp worst-...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1080/10556788.2019.1678033

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Balliol College
Role:
Author
ORCID:
0000-0002-0963-5550
More by this author
Role:
Author
ORCID:
0000-0002-1031-1588
Publisher:
Taylor and Francis
Journal:
Optimization Methods and Software More from this journal
Volume:
35
Issue:
2
Pages:
243-256
Publication date:
2019-10-24
Acceptance date:
2019-10-01
DOI:
EISSN:
1029-4937
ISSN:
1055-6788
Language:
English
Keywords:
Pubs id:
pubs:1067133
UUID:
uuid:09b543f4-83e2-4e03-9846-84cab74dad6c
Local pid:
pubs:1067133
Source identifiers:
1067133
Deposit date:
2019-11-23

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