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 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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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 |
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convex minimization |
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signal processing |
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1st Author's Name |
Masao Yamagishi |
1st Author's Affiliation |
Tokyo Institute of Technology (Tokyo Inst. of Tech) |
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Isao Yamada |
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Tokyo Institute of Technology (Tokyo Inst. of Tech) |
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Speaker |
Author-1 |
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 |
6 |
Date of Issue |
2011-02-24 (CAS, SIP, CS) |
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