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A Complexity-Based Review on Proximal Gradient Methods for Convex Composite Optimization

Author(s):

S. Richter, M. Morari, C. Jones
Conference/Journal:

vol. AUT12-01
Abstract:

The proximal gradient method and its accelerated variants represent recent generalizations of the gradient and fast gradient methods for convex composite minimization where the objective is represented as the sum of a smooth and a potentially nonsmooth function. These methods can be understood as exploiting the additive structure of the composite problem and hence are able to break the black box lower complexity bounds of first-order methods for nonsmooth convex optimization. This tutorial-style paper aims at highlighting the necessary background in complexity theory such that thereafter both the strength and significance of the proximal gradient method and its accelerated variants can be assessed from a complexity point of view.

Further Information
Year:

2012
Type of Publication:

(04)Technical Report
Supervisor:

M. Morari

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% Autogenerated BibTeX entry
@TechReport { RicMor:2012:IFA_4038,
    author={S. Richter and M. Morari and C. Jones},
    title={{A Complexity-Based Review on Proximal Gradient Methods for
	  Convex Composite Optimization}},
    institution={},
    year={2012},
    number={},
    address={},
    month=mar,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=4038}
}
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