First-order methods of smooth convex optimization with inexact oracle

We introduce the notion of inexact first-order oracle and analyze the behavior of several first-order methods of smooth convex optimization used with such an oracle. This notion of inexact oracle naturally appears in the context of smoothing techniques, Moreau–Yosida regularization, Augmented Lagran...

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Bibliographic Details
Published in:	Mathematical programming Vol. 146; no. 1-2; pp. 37 - 75
Main Authors:	Devolder, Olivier, Glineur, François, Nesterov, Yurii
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014 Springer Nature B.V
Subjects:	Accuracy Analysis Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Complexity theory Convex analysis Estimates Full Length Paper Functions (mathematics) Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Permissible error Regularization Smoothing Studies Theoretical Gradient methods Fast gradient methods 90C25 90C06 Inexact oracle Complexity bounds 90C60 First-order methods Smooth convex optimization
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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