Accelerated Bregman proximal gradient methods for relatively smooth convex optimization
Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance g...
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Gespeichert in:
| Autor*in: |
Hanzely, Filip [verfasserIn] Richtárik, Peter [verfasserIn] Xiao, Lin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Computational optimization and applications - New York, NY [u.a.] : Springer Science + Business Media B.V., 1992, 79(2021), 2 vom: 07. Apr., Seite 405-440 |
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| Übergeordnetes Werk: |
volume:79 ; year:2021 ; number:2 ; day:07 ; month:04 ; pages:405-440 |
| Links: |
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| DOI / URN: |
10.1007/s10589-021-00273-8 |
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SPR043960413 |
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| 520 | |a Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. | ||
| 650 | 4 | |a Convex optimization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Relative smoothness |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bregman divergence |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Proximal gradient methods |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Accelerated gradient methods |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Richtárik, Peter |e verfasserin |4 aut | |
| 700 | 1 | |a Xiao, Lin |e verfasserin |4 aut | |
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10.1007/s10589-021-00273-8 doi (DE-627)SPR043960413 (DE-599)SPRs10589-021-00273-8-e (SPR)s10589-021-00273-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl 54.80 bkl Hanzely, Filip verfasserin aut Accelerated Bregman proximal gradient methods for relatively smooth convex optimization 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. Convex optimization (dpeaa)DE-He213 Relative smoothness (dpeaa)DE-He213 Bregman divergence (dpeaa)DE-He213 Proximal gradient methods (dpeaa)DE-He213 Accelerated gradient methods (dpeaa)DE-He213 Richtárik, Peter verfasserin aut Xiao, Lin verfasserin aut Enthalten in Computational optimization and applications New York, NY [u.a.] : Springer Science + Business Media B.V., 1992 79(2021), 2 vom: 07. Apr., Seite 405-440 (DE-627)266881297 (DE-600)1467967-X 1573-2894 nnns volume:79 year:2021 number:2 day:07 month:04 pages:405-440 https://dx.doi.org/10.1007/s10589-021-00273-8 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_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 54.80 ASE AR 79 2021 2 07 04 405-440 |
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10.1007/s10589-021-00273-8 doi (DE-627)SPR043960413 (DE-599)SPRs10589-021-00273-8-e (SPR)s10589-021-00273-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl 54.80 bkl Hanzely, Filip verfasserin aut Accelerated Bregman proximal gradient methods for relatively smooth convex optimization 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. Convex optimization (dpeaa)DE-He213 Relative smoothness (dpeaa)DE-He213 Bregman divergence (dpeaa)DE-He213 Proximal gradient methods (dpeaa)DE-He213 Accelerated gradient methods (dpeaa)DE-He213 Richtárik, Peter verfasserin aut Xiao, Lin verfasserin aut Enthalten in Computational optimization and applications New York, NY [u.a.] : Springer Science + Business Media B.V., 1992 79(2021), 2 vom: 07. Apr., Seite 405-440 (DE-627)266881297 (DE-600)1467967-X 1573-2894 nnns volume:79 year:2021 number:2 day:07 month:04 pages:405-440 https://dx.doi.org/10.1007/s10589-021-00273-8 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_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 54.80 ASE AR 79 2021 2 07 04 405-440 |
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10.1007/s10589-021-00273-8 doi (DE-627)SPR043960413 (DE-599)SPRs10589-021-00273-8-e (SPR)s10589-021-00273-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl 54.80 bkl Hanzely, Filip verfasserin aut Accelerated Bregman proximal gradient methods for relatively smooth convex optimization 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. Convex optimization (dpeaa)DE-He213 Relative smoothness (dpeaa)DE-He213 Bregman divergence (dpeaa)DE-He213 Proximal gradient methods (dpeaa)DE-He213 Accelerated gradient methods (dpeaa)DE-He213 Richtárik, Peter verfasserin aut Xiao, Lin verfasserin aut Enthalten in Computational optimization and applications New York, NY [u.a.] : Springer Science + Business Media B.V., 1992 79(2021), 2 vom: 07. Apr., Seite 405-440 (DE-627)266881297 (DE-600)1467967-X 1573-2894 nnns volume:79 year:2021 number:2 day:07 month:04 pages:405-440 https://dx.doi.org/10.1007/s10589-021-00273-8 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_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 54.80 ASE AR 79 2021 2 07 04 405-440 |
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10.1007/s10589-021-00273-8 doi (DE-627)SPR043960413 (DE-599)SPRs10589-021-00273-8-e (SPR)s10589-021-00273-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl 54.80 bkl Hanzely, Filip verfasserin aut Accelerated Bregman proximal gradient methods for relatively smooth convex optimization 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. Convex optimization (dpeaa)DE-He213 Relative smoothness (dpeaa)DE-He213 Bregman divergence (dpeaa)DE-He213 Proximal gradient methods (dpeaa)DE-He213 Accelerated gradient methods (dpeaa)DE-He213 Richtárik, Peter verfasserin aut Xiao, Lin verfasserin aut Enthalten in Computational optimization and applications New York, NY [u.a.] : Springer Science + Business Media B.V., 1992 79(2021), 2 vom: 07. Apr., Seite 405-440 (DE-627)266881297 (DE-600)1467967-X 1573-2894 nnns volume:79 year:2021 number:2 day:07 month:04 pages:405-440 https://dx.doi.org/10.1007/s10589-021-00273-8 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_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 54.80 ASE AR 79 2021 2 07 04 405-440 |
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10.1007/s10589-021-00273-8 doi (DE-627)SPR043960413 (DE-599)SPRs10589-021-00273-8-e (SPR)s10589-021-00273-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl 54.80 bkl Hanzely, Filip verfasserin aut Accelerated Bregman proximal gradient methods for relatively smooth convex optimization 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. Convex optimization (dpeaa)DE-He213 Relative smoothness (dpeaa)DE-He213 Bregman divergence (dpeaa)DE-He213 Proximal gradient methods (dpeaa)DE-He213 Accelerated gradient methods (dpeaa)DE-He213 Richtárik, Peter verfasserin aut Xiao, Lin verfasserin aut Enthalten in Computational optimization and applications New York, NY [u.a.] : Springer Science + Business Media B.V., 1992 79(2021), 2 vom: 07. Apr., Seite 405-440 (DE-627)266881297 (DE-600)1467967-X 1573-2894 nnns volume:79 year:2021 number:2 day:07 month:04 pages:405-440 https://dx.doi.org/10.1007/s10589-021-00273-8 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_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 54.80 ASE AR 79 2021 2 07 04 405-440 |
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Enthalten in Computational optimization and applications 79(2021), 2 vom: 07. Apr., Seite 405-440 volume:79 year:2021 number:2 day:07 month:04 pages:405-440 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR043960413</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110225659.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">210507s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10589-021-00273-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR043960413</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)SPRs10589-021-00273-8-e</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10589-021-00273-8-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.80</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.80</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hanzely, Filip</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Accelerated Bregman proximal gradient methods for relatively smooth convex optimization</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex optimization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Relative smoothness</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bregman divergence</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proximal gradient methods</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Accelerated gradient methods</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Richtárik, Peter</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Xiao, Lin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Computational optimization and applications</subfield><subfield code="d">New York, NY [u.a.] : Springer Science + Business Media B.V., 1992</subfield><subfield code="g">79(2021), 2 vom: 07. 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Hanzely, Filip |
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Hanzely, Filip ddc 510 bkl 31.80 bkl 54.80 misc Convex optimization misc Relative smoothness misc Bregman divergence misc Proximal gradient methods misc Accelerated gradient methods Accelerated Bregman proximal gradient methods for relatively smooth convex optimization |
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510 ASE 31.80 bkl 54.80 bkl Accelerated Bregman proximal gradient methods for relatively smooth convex optimization Convex optimization (dpeaa)DE-He213 Relative smoothness (dpeaa)DE-He213 Bregman divergence (dpeaa)DE-He213 Proximal gradient methods (dpeaa)DE-He213 Accelerated gradient methods (dpeaa)DE-He213 |
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accelerated bregman proximal gradient methods for relatively smooth convex optimization |
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Accelerated Bregman proximal gradient methods for relatively smooth convex optimization |
| abstract |
Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. |
| abstractGer |
Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. |
| abstract_unstemmed |
Abstract We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an %$O(k^{-\gamma })%$ convergence rate, where %$\gamma \in (0,2]%$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have %$\gamma =2%$ and recover the convergence rate of Nesterov’s accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say %$\gamma \le 1%$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical %$O(k^{-2})%$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates. |
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| container_issue |
2 |
| title_short |
Accelerated Bregman proximal gradient methods for relatively smooth convex optimization |
| url |
https://dx.doi.org/10.1007/s10589-021-00273-8 |
| remote_bool |
true |
| author2 |
Richtárik, Peter Xiao, Lin |
| author2Str |
Richtárik, Peter Xiao, Lin |
| ppnlink |
266881297 |
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c |
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false |
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| doi_str |
10.1007/s10589-021-00273-8 |
| up_date |
2024-07-03T22:02:48.387Z |
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1803597033912664065 |
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|
| score |
7.401991 |