On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications
Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence t...
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| Autor*in: |
Yatakoat, Pornsak [verfasserIn] |
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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© The Author(s) 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Advances in difference equations - [S.l.] : Springer International, 2004, 2022(2022), 1 vom: 17. März |
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volume:2022 ; year:2022 ; number:1 ; day:17 ; month:03 |
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10.1186/s13662-022-03698-5 |
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| 520 | |a Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. | ||
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10.1186/s13662-022-03698-5 doi (DE-627)SPR046518622 (SPR)s13662-022-03698-5-e DE-627 ger DE-627 rakwb eng Yatakoat, Pornsak verfasserin aut On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. Convex minimization problems (dpeaa)DE-He213 Fixed points (dpeaa)DE-He213 Forward–backward algorithms (dpeaa)DE-He213 Image restoration problems (dpeaa)DE-He213 Suantai, Suthep aut Hanjing, Adisak aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2022(2022), 1 vom: 17. März (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2022 year:2022 number:1 day:17 month:03 https://dx.doi.org/10.1186/s13662-022-03698-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_206 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4305 AR 2022 2022 1 17 03 |
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10.1186/s13662-022-03698-5 doi (DE-627)SPR046518622 (SPR)s13662-022-03698-5-e DE-627 ger DE-627 rakwb eng Yatakoat, Pornsak verfasserin aut On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. Convex minimization problems (dpeaa)DE-He213 Fixed points (dpeaa)DE-He213 Forward–backward algorithms (dpeaa)DE-He213 Image restoration problems (dpeaa)DE-He213 Suantai, Suthep aut Hanjing, Adisak aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2022(2022), 1 vom: 17. März (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2022 year:2022 number:1 day:17 month:03 https://dx.doi.org/10.1186/s13662-022-03698-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_206 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4305 AR 2022 2022 1 17 03 |
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10.1186/s13662-022-03698-5 doi (DE-627)SPR046518622 (SPR)s13662-022-03698-5-e DE-627 ger DE-627 rakwb eng Yatakoat, Pornsak verfasserin aut On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. Convex minimization problems (dpeaa)DE-He213 Fixed points (dpeaa)DE-He213 Forward–backward algorithms (dpeaa)DE-He213 Image restoration problems (dpeaa)DE-He213 Suantai, Suthep aut Hanjing, Adisak aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2022(2022), 1 vom: 17. März (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2022 year:2022 number:1 day:17 month:03 https://dx.doi.org/10.1186/s13662-022-03698-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_206 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4305 AR 2022 2022 1 17 03 |
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10.1186/s13662-022-03698-5 doi (DE-627)SPR046518622 (SPR)s13662-022-03698-5-e DE-627 ger DE-627 rakwb eng Yatakoat, Pornsak verfasserin aut On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. Convex minimization problems (dpeaa)DE-He213 Fixed points (dpeaa)DE-He213 Forward–backward algorithms (dpeaa)DE-He213 Image restoration problems (dpeaa)DE-He213 Suantai, Suthep aut Hanjing, Adisak aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2022(2022), 1 vom: 17. März (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2022 year:2022 number:1 day:17 month:03 https://dx.doi.org/10.1186/s13662-022-03698-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_206 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4305 AR 2022 2022 1 17 03 |
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on some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications |
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On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications |
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Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. © The Author(s) 2022 |
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Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. © The Author(s) 2022 |
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Abstract In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others. © The Author(s) 2022 |
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Suantai, Suthep Hanjing, Adisak |
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Suantai, Suthep Hanjing, Adisak |
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377755699 |
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| doi_str |
10.1186/s13662-022-03698-5 |
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2024-07-03T23:01:26.842Z |
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