Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method
Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition gu...
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| Autor*in: |
Zhu, Daoli [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
Level-set subdifferential error bound |
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| Systematik: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of optimization theory and applications - Springer US, 1967, 189(2021), 3 vom: 31. Mai, Seite 889-918 |
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| Übergeordnetes Werk: |
volume:189 ; year:2021 ; number:3 ; day:31 ; month:05 ; pages:889-918 |
| Links: |
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| DOI / URN: |
10.1007/s10957-021-01865-4 |
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OLC2126108708 |
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| 520 | |a Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. | ||
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10.1007/s10957-021-01865-4 doi (DE-627)OLC2126108708 (DE-He213)s10957-021-01865-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Zhu, Daoli verfasserin aut Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. Level-set subdifferential error bound Variable Bregman proximal gradient method Linear convergence Bregman proximal error bound Deng, Sien (orcid)0000-0003-3453-6121 aut Li, Minghua aut Zhao, Lei aut Enthalten in Journal of optimization theory and applications Springer US, 1967 189(2021), 3 vom: 31. Mai, Seite 889-918 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:189 year:2021 number:3 day:31 month:05 pages:889-918 https://doi.org/10.1007/s10957-021-01865-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 189 2021 3 31 05 889-918 |
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10.1007/s10957-021-01865-4 doi (DE-627)OLC2126108708 (DE-He213)s10957-021-01865-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Zhu, Daoli verfasserin aut Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. Level-set subdifferential error bound Variable Bregman proximal gradient method Linear convergence Bregman proximal error bound Deng, Sien (orcid)0000-0003-3453-6121 aut Li, Minghua aut Zhao, Lei aut Enthalten in Journal of optimization theory and applications Springer US, 1967 189(2021), 3 vom: 31. Mai, Seite 889-918 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:189 year:2021 number:3 day:31 month:05 pages:889-918 https://doi.org/10.1007/s10957-021-01865-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 189 2021 3 31 05 889-918 |
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10.1007/s10957-021-01865-4 doi (DE-627)OLC2126108708 (DE-He213)s10957-021-01865-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Zhu, Daoli verfasserin aut Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. Level-set subdifferential error bound Variable Bregman proximal gradient method Linear convergence Bregman proximal error bound Deng, Sien (orcid)0000-0003-3453-6121 aut Li, Minghua aut Zhao, Lei aut Enthalten in Journal of optimization theory and applications Springer US, 1967 189(2021), 3 vom: 31. Mai, Seite 889-918 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:189 year:2021 number:3 day:31 month:05 pages:889-918 https://doi.org/10.1007/s10957-021-01865-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2030 SA 6420 SA 6420 AR 189 2021 3 31 05 889-918 |
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Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method |
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Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method |
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Zhu, Daoli |
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Journal of optimization theory and applications |
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Journal of optimization theory and applications |
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Zhu, Daoli Deng, Sien Li, Minghua Zhao, Lei |
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Zhu, Daoli |
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10.1007/s10957-021-01865-4 |
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330 510 000 |
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level-set subdifferential error bounds and linear convergence of bregman proximal gradient method |
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Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method |
| abstract |
Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
| abstractGer |
Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract In this work, we develop a level-set subdifferential error bound condition with an eye toward convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It is proved that the aforementioned condition guarantees linear convergence of VBPG and is weaker than Kurdyka–Łojasiewicz property, weak metric subregularity, and Bregman proximal error bound. Along the way, we are able to derive a number of verifiable conditions for level-set subdifferential error bounds to hold, and necessary conditions and sufficient conditions for linear convergence relative to a level set for nonsmooth and nonconvex optimization problems. The newly established results not only enable us to show that any accumulation point of the sequence generated by VBPG is at least a critical point of the limiting subdifferential or even a critical point of the proximal subdifferential with a fixed Bregman function in each iteration, but also provide a fresh perspective that allows us to explore inner-connections among many known sufficient conditions for linear convergence of various first-order methods. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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Level-Set Subdifferential Error Bounds and Linear Convergence of Bregman Proximal Gradient Method |
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https://doi.org/10.1007/s10957-021-01865-4 |
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Deng, Sien Li, Minghua Zhao, Lei |
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