The Forward–Backward Algorithm and the Normal Problem
Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions u...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Moursi, Walaa M. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of optimization theory and applications - Dordrecht [u.a.] : Springer Science + Business Media, 1967, 176(2018), 3 vom: 06. Feb., Seite 605-624 |
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| Übergeordnetes Werk: |
volume:176 ; year:2018 ; number:3 ; day:06 ; month:02 ; pages:605-624 |
| Links: |
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| DOI / URN: |
10.1007/s10957-017-1113-4 |
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| Katalog-ID: |
SPR015014886 |
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| 245 | 1 | 4 | |a The Forward–Backward Algorithm and the Normal Problem |
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| 520 | |a Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. | ||
| 650 | 4 | |a Attouch–Théra duality |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Firmly nonexpansive mapping |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fixed point |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Forward–backward splitting operator |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Normal problem |7 (dpeaa)DE-He213 | |
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10.1007/s10957-017-1113-4 doi (DE-627)SPR015014886 (SPR)s10957-017-1113-4-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Moursi, Walaa M. verfasserin aut The Forward–Backward Algorithm and the Normal Problem 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. Attouch–Théra duality (dpeaa)DE-He213 Firmly nonexpansive mapping (dpeaa)DE-He213 Fixed point (dpeaa)DE-He213 Forward–backward splitting operator (dpeaa)DE-He213 Normal problem (dpeaa)DE-He213 Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 176(2018), 3 vom: 06. Feb., Seite 605-624 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:176 year:2018 number:3 day:06 month:02 pages:605-624 https://dx.doi.org/10.1007/s10957-017-1113-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 176 2018 3 06 02 605-624 |
| spelling |
10.1007/s10957-017-1113-4 doi (DE-627)SPR015014886 (SPR)s10957-017-1113-4-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Moursi, Walaa M. verfasserin aut The Forward–Backward Algorithm and the Normal Problem 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. Attouch–Théra duality (dpeaa)DE-He213 Firmly nonexpansive mapping (dpeaa)DE-He213 Fixed point (dpeaa)DE-He213 Forward–backward splitting operator (dpeaa)DE-He213 Normal problem (dpeaa)DE-He213 Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 176(2018), 3 vom: 06. Feb., Seite 605-624 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:176 year:2018 number:3 day:06 month:02 pages:605-624 https://dx.doi.org/10.1007/s10957-017-1113-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 176 2018 3 06 02 605-624 |
| allfields_unstemmed |
10.1007/s10957-017-1113-4 doi (DE-627)SPR015014886 (SPR)s10957-017-1113-4-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Moursi, Walaa M. verfasserin aut The Forward–Backward Algorithm and the Normal Problem 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. Attouch–Théra duality (dpeaa)DE-He213 Firmly nonexpansive mapping (dpeaa)DE-He213 Fixed point (dpeaa)DE-He213 Forward–backward splitting operator (dpeaa)DE-He213 Normal problem (dpeaa)DE-He213 Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 176(2018), 3 vom: 06. Feb., Seite 605-624 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:176 year:2018 number:3 day:06 month:02 pages:605-624 https://dx.doi.org/10.1007/s10957-017-1113-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 176 2018 3 06 02 605-624 |
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10.1007/s10957-017-1113-4 doi (DE-627)SPR015014886 (SPR)s10957-017-1113-4-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Moursi, Walaa M. verfasserin aut The Forward–Backward Algorithm and the Normal Problem 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. Attouch–Théra duality (dpeaa)DE-He213 Firmly nonexpansive mapping (dpeaa)DE-He213 Fixed point (dpeaa)DE-He213 Forward–backward splitting operator (dpeaa)DE-He213 Normal problem (dpeaa)DE-He213 Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 176(2018), 3 vom: 06. Feb., Seite 605-624 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:176 year:2018 number:3 day:06 month:02 pages:605-624 https://dx.doi.org/10.1007/s10957-017-1113-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 176 2018 3 06 02 605-624 |
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10.1007/s10957-017-1113-4 doi (DE-627)SPR015014886 (SPR)s10957-017-1113-4-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Moursi, Walaa M. verfasserin aut The Forward–Backward Algorithm and the Normal Problem 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. Attouch–Théra duality (dpeaa)DE-He213 Firmly nonexpansive mapping (dpeaa)DE-He213 Fixed point (dpeaa)DE-He213 Forward–backward splitting operator (dpeaa)DE-He213 Normal problem (dpeaa)DE-He213 Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 176(2018), 3 vom: 06. Feb., Seite 605-624 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:176 year:2018 number:3 day:06 month:02 pages:605-624 https://dx.doi.org/10.1007/s10957-017-1113-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 176 2018 3 06 02 605-624 |
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Enthalten in Journal of optimization theory and applications 176(2018), 3 vom: 06. Feb., Seite 605-624 volume:176 year:2018 number:3 day:06 month:02 pages:605-624 |
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Enthalten in Journal of optimization theory and applications 176(2018), 3 vom: 06. Feb., Seite 605-624 volume:176 year:2018 number:3 day:06 month:02 pages:605-624 |
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Moursi, Walaa M. @@aut@@ |
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The Forward–Backward Algorithm and the Normal Problem |
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Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. |
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Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. |
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Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory. |
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In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. 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