On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression
Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General...
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| Autor*in: |
Nakayama, Shummin [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Optimization letters - Springer Berlin Heidelberg, 2007, 15(2021), 8 vom: 03. März, Seite 2831-2860 |
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| Übergeordnetes Werk: |
volume:15 ; year:2021 ; number:8 ; day:03 ; month:03 ; pages:2831-2860 |
| Links: |
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| DOI / URN: |
10.1007/s11590-021-01716-1 |
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OLC2077017899 |
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| 520 | |a Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. | ||
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10.1007/s11590-021-01716-1 doi (DE-627)OLC2077017899 (DE-He213)s11590-021-01716-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Nakayama, Shummin verfasserin (orcid)0000-0001-7780-8348 aut On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. Proximal gradient method DC algorithms Proximal alternating linearized minimization D-stationary points Critical points Gotoh, Jun-ya (orcid)0000-0002-0097-7298 aut Enthalten in Optimization letters Springer Berlin Heidelberg, 2007 15(2021), 8 vom: 03. März, Seite 2831-2860 (DE-627)527562920 (DE-600)2274663-8 (DE-576)272713724 1862-4472 nnns volume:15 year:2021 number:8 day:03 month:03 pages:2831-2860 https://doi.org/10.1007/s11590-021-01716-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW GBV_ILN_267 GBV_ILN_2018 AR 15 2021 8 03 03 2831-2860 |
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10.1007/s11590-021-01716-1 doi (DE-627)OLC2077017899 (DE-He213)s11590-021-01716-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Nakayama, Shummin verfasserin (orcid)0000-0001-7780-8348 aut On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. Proximal gradient method DC algorithms Proximal alternating linearized minimization D-stationary points Critical points Gotoh, Jun-ya (orcid)0000-0002-0097-7298 aut Enthalten in Optimization letters Springer Berlin Heidelberg, 2007 15(2021), 8 vom: 03. März, Seite 2831-2860 (DE-627)527562920 (DE-600)2274663-8 (DE-576)272713724 1862-4472 nnns volume:15 year:2021 number:8 day:03 month:03 pages:2831-2860 https://doi.org/10.1007/s11590-021-01716-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW GBV_ILN_267 GBV_ILN_2018 AR 15 2021 8 03 03 2831-2860 |
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10.1007/s11590-021-01716-1 doi (DE-627)OLC2077017899 (DE-He213)s11590-021-01716-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Nakayama, Shummin verfasserin (orcid)0000-0001-7780-8348 aut On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. Proximal gradient method DC algorithms Proximal alternating linearized minimization D-stationary points Critical points Gotoh, Jun-ya (orcid)0000-0002-0097-7298 aut Enthalten in Optimization letters Springer Berlin Heidelberg, 2007 15(2021), 8 vom: 03. März, Seite 2831-2860 (DE-627)527562920 (DE-600)2274663-8 (DE-576)272713724 1862-4472 nnns volume:15 year:2021 number:8 day:03 month:03 pages:2831-2860 https://doi.org/10.1007/s11590-021-01716-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW GBV_ILN_267 GBV_ILN_2018 AR 15 2021 8 03 03 2831-2860 |
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10.1007/s11590-021-01716-1 doi (DE-627)OLC2077017899 (DE-He213)s11590-021-01716-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Nakayama, Shummin verfasserin (orcid)0000-0001-7780-8348 aut On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. Proximal gradient method DC algorithms Proximal alternating linearized minimization D-stationary points Critical points Gotoh, Jun-ya (orcid)0000-0002-0097-7298 aut Enthalten in Optimization letters Springer Berlin Heidelberg, 2007 15(2021), 8 vom: 03. März, Seite 2831-2860 (DE-627)527562920 (DE-600)2274663-8 (DE-576)272713724 1862-4472 nnns volume:15 year:2021 number:8 day:03 month:03 pages:2831-2860 https://doi.org/10.1007/s11590-021-01716-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW GBV_ILN_267 GBV_ILN_2018 AR 15 2021 8 03 03 2831-2860 |
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10.1007/s11590-021-01716-1 doi (DE-627)OLC2077017899 (DE-He213)s11590-021-01716-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Nakayama, Shummin verfasserin (orcid)0000-0001-7780-8348 aut On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. Proximal gradient method DC algorithms Proximal alternating linearized minimization D-stationary points Critical points Gotoh, Jun-ya (orcid)0000-0002-0097-7298 aut Enthalten in Optimization letters Springer Berlin Heidelberg, 2007 15(2021), 8 vom: 03. März, Seite 2831-2860 (DE-627)527562920 (DE-600)2274663-8 (DE-576)272713724 1862-4472 nnns volume:15 year:2021 number:8 day:03 month:03 pages:2831-2860 https://doi.org/10.1007/s11590-021-01716-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW GBV_ILN_267 GBV_ILN_2018 AR 15 2021 8 03 03 2831-2860 |
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on the superiority of pgms to pdcas in nonsmooth nonconvex sparse regression |
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On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression |
| abstract |
Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
| abstractGer |
Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical points. Recently some enhanced versions of PDCAs are shown to converge to d-stationary points, which are stronger necessary condition for local optimality than critical points. In this paper we claim that without any modification, PGMs converge to a d-stationary point not only to DC problems but also to more general nonsmooth nonconvex problems under some technical assumptions. While the convergence to d-stationary points is known for the case where the step size is small enough, the finding of this paper is valid also for extended versions such as GIST and its alternating optimization version, which is to be developed in this paper. Numerical results show that among several algorithms in the two categories, modified versions of PGM perform best among those not only in solution quality but also in computation time. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
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| title_short |
On the superiority of PGMs to PDCAs in nonsmooth nonconvex sparse regression |
| url |
https://doi.org/10.1007/s11590-021-01716-1 |
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| author2 |
Gotoh, Jun-ya |
| author2Str |
Gotoh, Jun-ya |
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2024-07-04T04:11:03.807Z |
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