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Paper Abstract and Keywords
Presentation 2011-03-03 10:00
Two improvements of the fast iterative shrinkage/thresholding algorithm -- Overrelaxation and weak convergence --
Masao Yamagishi, Isao Yamada (Tokyo Inst. of Tech) CAS2010-126 SIP2010-142 CS2010-96
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we present two improved schemes of FISTA (an iterative gradient-based algorithm, whose convergence rate of the objective function is $\mathcal{O}(1/k^2)$ in term of the iteration counter $k$) for the minimization of the sum of a smooth and a nonsmooth convex function. Such minimization problems arise naturally in signal and image processing. Our two schemes overcome two limitations of FISTA: (i) The stepsize in the forward-backward splitting step in FISTA is bounded by a constant value determined by the Lipschitz constant of the gradient of the smooth function and (ii) no results on weak convergence of FISTA to a solution had been presented to our best knowledge. The first scheme admits variable stepsizes in broader ranges than FISTA while keeping the same convergence rate $\mathcal{O}(1/k^2)$ of the objective function. The second scheme, whose convergence rate of the objective function is not guaranteed as $\mathcal{O}(1/k^2)$, converges weakly to a solution by using a sequence generated by FISTA. A numerical example demonstrates the effectiveness of each improvement by showing that the proposed schemes outperform conventional algorithms in terms of speed of convergence.
Keyword (in Japanese) (See Japanese page) 
(in English) acceleration / adaptive filtering / convergence / convex minimization / signal processing / / /  
Reference Info. IEICE Tech. Rep., vol. 110, no. 440, SIP2010-142, pp. 143-148, March 2011.
Paper # SIP2010-142 
Date of Issue 2011-02-24 (CAS, SIP, CS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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Download PDF CAS2010-126 SIP2010-142 CS2010-96

Conference Information
Committee CS SIP CAS  
Conference Date 2011-03-03 - 2011-03-04 
Place (in Japanese) (See Japanese page) 
Place (in English) Ohhamanobumoto memorial hall (Ishigaki)( 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Network Processor, Signal Processing for Communications, Wireless LAN/PAN, etc. 
Paper Information
Registration To SIP 
Conference Code 2011-03-CS-SIP-CAS 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Two improvements of the fast iterative shrinkage/thresholding algorithm 
Sub Title (in English) Overrelaxation and weak convergence 
Keyword(1) acceleration  
Keyword(2) adaptive filtering  
Keyword(3) convergence  
Keyword(4) convex minimization  
Keyword(5) signal processing  
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1st Author's Name Masao Yamagishi  
1st Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech)
2nd Author's Name Isao Yamada  
2nd Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech)
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Date Time 2011-03-03 10:00:00 
Presentation Time 20 minutes 
Registration for SIP 
Paper # CAS2010-126, SIP2010-142, CS2010-96 
Volume (vol) vol.110 
Number (no) no.439(CAS), no.440(SIP), no.441(CS) 
Page pp.143-148 
#Pages
Date of Issue 2011-02-24 (CAS, SIP, CS) 


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