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Second-order optimality and beyond: characterization and evaluation complexity in convexly-constrained nonlinear optimization

Abstract:

High-order optimality conditions for convexly-constrained nonlinear optimization problems are analyzed. A corresponding (expensive) measure of criticality for arbitrary order is proposed and extended to define high-order ∈-approximate critical points. This new measure is then used within a conceptual trust-region algorithm to show that, if deriva- tives of the objective function up to order q ≥ 1 can be evaluated and are Lipschitz continuous, then this algorithm applied to the convexly constr...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s10208-017-9363-y

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Institution:
University of Oxford
Oxford college:
Balliol College
Role:
Author
Italian National Institute of Higher Mathematics More from this funder
Belgian Fund for Scientific Research More from this funder
Hong Kong Polytechnic University More from this funder
Leverhulme Trust More from this funder
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Publisher:
Springer Publisher's website
Journal:
Foundations of Computational Mathematics Journal website
Publication date:
2017-09-01
Acceptance date:
2017-05-29
DOI:
EISSN:
1615-3383
ISSN:
1615-3375
Source identifiers:
709049
Keywords:
Pubs id:
pubs:709049
UUID:
uuid:3c1ac5c6-dfe3-4b5c-8123-e95e8ecba423
Local pid:
pubs:709049
Deposit date:
2017-07-23

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