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On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems.

Abstract:

It is shown that the steepest-descent and Newton's methods for unconstrained nonconvex optimization under standard assumptions may both require a number of iterations and function evaluations arbitrarily close to O(ε ?2) to drive the norm of the gradient below ε. This shows that the upper bound of O(ε ?2) evaluations known for the steepest descent is tight and that Newton's method may be as slow as the steepest-descent method in the worst case. The improved evaluation complexity bound of O(ε ...

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Publisher copy:
10.1137/090774100

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Gould, NIM More by this author
Journal:
SIAM Journal on Optimization
Volume:
20
Issue:
6
Pages:
2833-2852
Publication date:
2010
DOI:
EISSN:
1095-7189
ISSN:
1052-6234
URN:
uuid:2a7ae05b-7a16-4a51-b66d-80635fc06215
Source identifiers:
400607
Local pid:
pubs:400607

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