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en:intro:researches:fixedpoint [2016/03/31 20:39] – [Acceleration Algorithms for Solving Fixed Points] Hideaki IIDUKAen:intro:researches:fixedpoint [2018/07/02 10:29] (現在) – [Acceleration of the Krasnosel'skii-Mann Algorithm] Hideaki IIDUKA
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 ==== Acceleration of the Krasnosel'skii-Mann Algorithm ==== ==== Acceleration of the Krasnosel'skii-Mann Algorithm ====
 We numerically and theoretically compared our algorithm with the Krasnosel’skii-Mann algorithm and showed that it reduces the running time and iterations needed to find a fixed point compared with that algorithm. It is summarized as the following papers (You can get our papers from [[en:intro:publications|Publications]] page). We numerically and theoretically compared our algorithm with the Krasnosel’skii-Mann algorithm and showed that it reduces the running time and iterations needed to find a fixed point compared with that algorithm. It is summarized as the following papers (You can get our papers from [[en:intro:publications|Publications]] page).
-  * [[en:iiduka:|H. Iiduka]]: [[http://arxiv.org/abs/1509.05605| Line Search Fixed Point Algorithms Based on Nonlinear Conjugate Gradient Directions: Application to Constrained Smooth Convex Optimization]], submitted+  * K. Fujiwara and [[:en:iiduka:|H. Iiduka]]: [[http://www.ybook.co.jp/online2/oplna/vol3/p189.html|Modification of the Krasnosel'skii-Mann Fixed Point Algorithm by Using Three-term Conjugate Gradients]], Linear and Nonlinear Analysis, Vol. 3, No. 2, pp.189-202, 2017. 
-  * [[http://arnip.org/|K. Hishinuma]] and [[:iiduka:|H. Iiduka]]: [[http://www.ybook.co.jp/online-p/JNCA/Open/16/jncav16n11p2243-oa/FLASH/index.html|On Acceleration of the Krasnosel'skii-Mann Fixed Point Algorithm Based on Conjugate Gradient Method for Smooth Optimization]], Journal of Nonlinear and Convex Analysis: Special Issue-Dedicated to Wataru Takahashi on the occasion of his 70th birth day, Vol. 16, No. 11, pp. 2243-2254, 2015.+  * [[:en:iiduka:|H. Iiduka]]: [[http://fixedpointtheoryandapplications.springeropen.com/articles/10.1186/s13663-016-0567-7| Line Search Fixed Point Algorithms Based on Nonlinear Conjugate Gradient Directions: Application to Constrained Smooth Convex Optimization]], Fixed Point Theory and Applications, Vol. 2016, No. 77, 2016
 +  * K. Hishinuma and [[:en:iiduka:|H. Iiduka]]: [[http://www.ybook.co.jp/online-p/JNCA/Open/16/jncav16n11p2243-oa/FLASH/index.html|On Acceleration of the Krasnosel'skii-Mann Fixed Point Algorithm Based on Conjugate Gradient Method for Smooth Optimization]], Journal of Nonlinear and Convex Analysis: Special Issue-Dedicated to Wataru Takahashi on the occasion of his 70th birth day, Vol. 16, No. 11, pp. 2243-2254, 2015.
  
  
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   * [[en:iiduka:|H. Iiduka]]: [[http://www.sciencedirect.com/science/article/pii/S0096300311000099|Three-term Conjugate Gradient Method for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping]], Applied Mathematics and Computation, Vol. 217, No. 13, pp. 6315-6327, 2011.   * [[en:iiduka:|H. Iiduka]]: [[http://www.sciencedirect.com/science/article/pii/S0096300311000099|Three-term Conjugate Gradient Method for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping]], Applied Mathematics and Computation, Vol. 217, No. 13, pp. 6315-6327, 2011.
   * [[en:iiduka:|H. Iiduka]] and [[http://www.sp.ss.titech.ac.jp/index.php?Isao%20Yamada|I. Yamada]]: [[http://epubs.siam.org/action/showAbstract?page=1881&volume=19&issue=4&journalCode=sjope8|A Use of Conjugate Gradient Direction for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping]], SIAM Journal on Optimization, Vol. 19, No. 4, pp. 1881-1893, 2009.    * [[en:iiduka:|H. Iiduka]] and [[http://www.sp.ss.titech.ac.jp/index.php?Isao%20Yamada|I. Yamada]]: [[http://epubs.siam.org/action/showAbstract?page=1881&volume=19&issue=4&journalCode=sjope8|A Use of Conjugate Gradient Direction for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping]], SIAM Journal on Optimization, Vol. 19, No. 4, pp. 1881-1893, 2009. 
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