Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds

Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorit...
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Autor*in:	Feng, Shuailing [verfasserIn] Huang, Wen Song, Lele Ying, Shihui Zeng, Tieyong

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Proximal gradient method Hadamard manifolds Manifold optimization Convergence analysis

Anmerkung:	© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021

Übergeordnetes Werk:	Enthalten in: Optimization letters - Berlin : Springer, 2007, 16(2021), 8 vom: 06. Nov., Seite 2277-2297
Übergeordnetes Werk:	volume:16 ; year:2021 ; number:8 ; day:06 ; month:11 ; pages:2277-2297

Links:	Volltext

DOI / URN:	10.1007/s11590-021-01822-0

Katalog-ID:	SPR048296023

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allfields	10.1007/s11590-021-01822-0 doi (DE-627)SPR048296023 (SPR)s11590-021-01822-0-e DE-627 ger DE-627 rakwb eng Feng, Shuailing verfasserin aut Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. Proximal gradient method (dpeaa)DE-He213 Hadamard manifolds (dpeaa)DE-He213 Manifold optimization (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Huang, Wen aut Song, Lele aut Ying, Shihui (orcid)0000-0001-9423-0146 aut Zeng, Tieyong aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2021), 8 vom: 06. Nov., Seite 2277-2297 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297 https://dx.doi.org/10.1007/s11590-021-01822-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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 AR 16 2021 8 06 11 2277-2297
spelling	10.1007/s11590-021-01822-0 doi (DE-627)SPR048296023 (SPR)s11590-021-01822-0-e DE-627 ger DE-627 rakwb eng Feng, Shuailing verfasserin aut Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. Proximal gradient method (dpeaa)DE-He213 Hadamard manifolds (dpeaa)DE-He213 Manifold optimization (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Huang, Wen aut Song, Lele aut Ying, Shihui (orcid)0000-0001-9423-0146 aut Zeng, Tieyong aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2021), 8 vom: 06. Nov., Seite 2277-2297 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297 https://dx.doi.org/10.1007/s11590-021-01822-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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 AR 16 2021 8 06 11 2277-2297
allfields_unstemmed	10.1007/s11590-021-01822-0 doi (DE-627)SPR048296023 (SPR)s11590-021-01822-0-e DE-627 ger DE-627 rakwb eng Feng, Shuailing verfasserin aut Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. Proximal gradient method (dpeaa)DE-He213 Hadamard manifolds (dpeaa)DE-He213 Manifold optimization (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Huang, Wen aut Song, Lele aut Ying, Shihui (orcid)0000-0001-9423-0146 aut Zeng, Tieyong aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2021), 8 vom: 06. Nov., Seite 2277-2297 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297 https://dx.doi.org/10.1007/s11590-021-01822-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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 AR 16 2021 8 06 11 2277-2297
allfieldsGer	10.1007/s11590-021-01822-0 doi (DE-627)SPR048296023 (SPR)s11590-021-01822-0-e DE-627 ger DE-627 rakwb eng Feng, Shuailing verfasserin aut Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. Proximal gradient method (dpeaa)DE-He213 Hadamard manifolds (dpeaa)DE-He213 Manifold optimization (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Huang, Wen aut Song, Lele aut Ying, Shihui (orcid)0000-0001-9423-0146 aut Zeng, Tieyong aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2021), 8 vom: 06. Nov., Seite 2277-2297 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297 https://dx.doi.org/10.1007/s11590-021-01822-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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 AR 16 2021 8 06 11 2277-2297
allfieldsSound	10.1007/s11590-021-01822-0 doi (DE-627)SPR048296023 (SPR)s11590-021-01822-0-e DE-627 ger DE-627 rakwb eng Feng, Shuailing verfasserin aut Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. Proximal gradient method (dpeaa)DE-He213 Hadamard manifolds (dpeaa)DE-He213 Manifold optimization (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213 Huang, Wen aut Song, Lele aut Ying, Shihui (orcid)0000-0001-9423-0146 aut Zeng, Tieyong aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2021), 8 vom: 06. Nov., Seite 2277-2297 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297 https://dx.doi.org/10.1007/s11590-021-01822-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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 AR 16 2021 8 06 11 2277-2297
language	English
source	Enthalten in Optimization letters 16(2021), 8 vom: 06. Nov., Seite 2277-2297 volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297
sourceStr	Enthalten in Optimization letters 16(2021), 8 vom: 06. Nov., Seite 2277-2297 volume:16 year:2021 number:8 day:06 month:11 pages:2277-2297
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Proximal gradient method Hadamard manifolds Manifold optimization Convergence analysis
isfreeaccess_bool	false
container_title	Optimization letters
authorswithroles_txt_mv	Feng, Shuailing @@aut@@ Huang, Wen @@aut@@ Song, Lele @@aut@@ Ying, Shihui @@aut@@ Zeng, Tieyong @@aut@@
publishDateDaySort_date	2021-11-06T00:00:00Z
hierarchy_top_id	534676499
id	SPR048296023
language_de	englisch
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author	Feng, Shuailing
spellingShingle	Feng, Shuailing misc Proximal gradient method misc Hadamard manifolds misc Manifold optimization misc Convergence analysis Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds
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topic_title	Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds Proximal gradient method (dpeaa)DE-He213 Hadamard manifolds (dpeaa)DE-He213 Manifold optimization (dpeaa)DE-He213 Convergence analysis (dpeaa)DE-He213
topic	misc Proximal gradient method misc Hadamard manifolds misc Manifold optimization misc Convergence analysis
topic_unstemmed	misc Proximal gradient method misc Hadamard manifolds misc Manifold optimization misc Convergence analysis
topic_browse	misc Proximal gradient method misc Hadamard manifolds misc Manifold optimization misc Convergence analysis
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title	Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds
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title_full	Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds
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title_sort	proximal gradient method for nonconvex and nonsmooth optimization on hadamard manifolds
title_auth	Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds
abstract	Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
abstractGer	Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
abstract_unstemmed	Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
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title_short	Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds
url	https://dx.doi.org/10.1007/s11590-021-01822-0
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up_date	2024-07-03T18:18:19.439Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR048296023</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509113230.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">221007s2021 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11590-021-01822-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR048296023</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11590-021-01822-0-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="100" ind1="1" ind2=" "><subfield code="a">Feng, Shuailing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds</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="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we address the minimizing problem of the nonconvex and nonsmooth functions on Hadamard manifolds, and develop an improved proximal gradient method. First, by utilizing the geometric structure of non-positive curvature manifolds, we propose a monotone proximal gradient algorithm with fixed step size on Hadamard manifolds. Then, a convergence theorem of the proposed method has been established under the reasonable definition of proximal gradient mapping on manifolds. If the function further satisfies the Riemannian Kurdyka-Łojasiewicz (KL) property with an exponent, the local convergence rate is given. Finally, numerical experiments on a special Hadamard manifold, named symmetric positive definite matrix manifold, show the advantages of the proposed method.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proximal gradient method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hadamard manifolds</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Manifold optimization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convergence analysis</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Huang, Wen</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Song, Lele</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ying, Shihui</subfield><subfield code="0">(orcid)0000-0001-9423-0146</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zeng, Tieyong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Optimization letters</subfield><subfield code="d">Berlin : Springer, 2007</subfield><subfield code="g">16(2021), 8 vom: 06. 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Proximal gradient method for nonconvex and nonsmooth optimization on Hadamard manifolds

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