Universal regularization methods-varying the power, the smoothness and the accuracy

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Persistent URL	http://purl.org/net/epubs/work/30813095
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Record Id	30813095
Title	Universal regularization methods-varying the power, the smoothness and the accuracy
Contributors	C Cartis (STFC Rutherford Appleton Lab.), NIM Gould (STFC Rutherford Appleton Lab.), PL Toint
Abstract	Adaptive cubic regularization methods have emerged as a credible alternative to line search and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of adaptive regularization methods, that use first or higher-order local Taylor models of the objective regularized by a(ny) power of the step size and applied to convexly-constrained optimization problems. We investigate the worst-case evaluation complexity/global rate of convergence of these algorithms, when the level of sufficient smoothness of the objective may be unknown or may even be absent. We find that the methods accurately reflect in their complexity the degree of smoothness of the objective and satisfy increasingly better bounds with improving accuracy of the models. The bounds vary continuously and robustly with respect to the regularization power and accuracy of the model and the degree of smoothness of the objective.
Organisation	STFC , SCI-COMP , SCI-COMP-CM
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Funding Information
Related Research Object(s):	42187182
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	RAL Preprints RAL-P-2016-010, SIAM J Optimiz 2016.		RAL-P-2016-010.pdf	2016