| No | 207426 |
|---|---|
| 標題（和） | Two improvements of the fast iterative shrinkage/thresholding algorithm --Overrelaxation and weak convergence-- |
| 標題（英） | Two improvements of the fast iterative shrinkage/thresholding algorithm --Overrelaxation and weak convergence-- |
| 研究会名（和） | 通信方式, 信号処理, 回路とシステム |
| 研究会名（英） | Communication Systems, Signal Processing, Circuits and Systems |
| 開催年月日 | 2011-03-03 |
| 終了年月日 | 2011-03-04 |
| 会議種別コード | 5 |
| 共催団体名（和） | |
| 資料番号 | CAS2010-126, SIP2010-142, CS2010-96 |
| 抄録（和） | |
| 抄録（英） | 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. |
| 収録資料名（和） | 電子情報通信学会技術研究報告 |
| 収録資料の巻号 | Vol.110, No.439,440,441 |
| ページ開始 | 143 |
| ページ終了 | 148 |
| キーワード（和） | |
| キーワード（英） | acceleration,adaptive filtering,convergence,convex minimization,signal processing |
| 本文の言語 | ENG |
| 著者（和） | 山岸昌夫 |
| 著者（ヨミ） | ヤマギシ マサオ |
| 著者（英） | Masao Yamagishi |
| 所属機関（和） | 東京工業大学 |
| 所属機関（英） | Tokyo Institute of Technology |
| 著者（和） | 山田功 |
| 著者（ヨミ） | ヤマダ イサオ |
| 著者（英） | Isao Yamada |
| 所属機関（和） | 東京工業大学 |
| 所属機関（英） | Tokyo Institute of Technology |