Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

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Persistent URL	http://purl.org/net/epubs/work/12297414
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Record Id	12297414
Title	Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
Contributors	C Cartis (Oxford U.), NIM Gould (STFC Rutherford Appleton Lab.), PL Toint (University of Namur, Belgium)
Abstract	The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined threshold. The analysis covers the entire range of meaningful powers in the regularization term as well as for the Hölder exponent for the gradient. The resulting complexity bounds vary according to the regularization power and the assumed Hölder exponent, recovering known results when available.
Organisation	STFC , SCI-COMP , SCI-COMP-CM
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Related Research Object(s):	36256611
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	RAL-P-2014-014, Optim Method Softw 2014.		RAL-P-2014-014.pdf	2014