Modified Fejér sequences and applications

In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for o...

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Bibliographic Details
Main Authors: Lin, Junhong (Author), Rosasco, Lorenzo (Contributor), Villa, Silvia (Author), Zhou, Ding-Xuan (Author)
Other Authors: Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences (Contributor)
Format: Article
Language:English
Published: Springer US, 2018-08-14T17:52:33Z.
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Online Access:Get fulltext
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520 |a In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for objective function values of several optimization algorithms. In particular, our results apply to forward-backward splitting algorithm, incremental subgradient proximal algorithm, and the Douglas-Rachford splitting method including and generalizing known results. 
520 |a Italy. Ministry of Education, University, Scientific and Technological Research (FIRB Project RBFR12M3AC) 
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655 7 |a Article 
773 |t Computational Optimization and Applications