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Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models

Abstract:

Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of O(∈−3/2) proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an ∈-approximate first-order critical point can be obtained under significantly weaker assumptions. Moreover, the result is generalized to the case where high-order derivatives are used, resulting in a bound of O(∈−(p+1)/p) evaluations whenever derivatives of order p are available...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/978-3-030-12767-1

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
Belgian Fund for Scientific Research More from this funder
Leverhulme Trust More from this funder
Balliol College (Oxford) More from this funder
Publisher:
Springer Publisher's website
Journal:
Springer Optimization and Its Applications Journal website
Volume:
145
Series:
Springer Optimization and Its Applications
Host title:
Approximation and Optimization: Algorithms, Complexity and Applications
Publication date:
2019-01-01
Acceptance date:
2018-07-16
Event location:
Athens, Greece
DOI:
ISSN:
1931-6828
Source identifiers:
951522
ISBN:
9783030127671
Keywords:
Pubs id:
pubs:951522
UUID:
uuid:1305118d-dc1b-4b43-a062-65102090a1f6
Local pid:
pubs:951522
Deposit date:
2018-12-11

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