A note on the spectral gradient projection method for nonlinear monotone equations with applications

Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direct...
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Autor*in:	Abubakar, Auwal Bala [verfasserIn] Kumam, Poom [verfasserIn] Mohammad, Hassan [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Nonlinear monotone equations Spectral gradient method Projection method Global convergence Compressive sensing

Übergeordnetes Werk:	Enthalten in: Computational and applied mathematics - Berlin : Springer, 2003, 39(2020), 2 vom: 18. Apr.
Übergeordnetes Werk:	volume:39 ; year:2020 ; number:2 ; day:18 ; month:04

Links:	Volltext

DOI / URN:	10.1007/s40314-020-01151-5

Katalog-ID:	SPR039444139

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520			\|a Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing.
650		4	\|a Nonlinear monotone equations \|7 (dpeaa)DE-He213
650		4	\|a Spectral gradient method \|7 (dpeaa)DE-He213
650		4	\|a Projection method \|7 (dpeaa)DE-He213
650		4	\|a Global convergence \|7 (dpeaa)DE-He213
650		4	\|a Compressive sensing \|7 (dpeaa)DE-He213
700	1		\|a Kumam, Poom \|e verfasserin \|4 aut
700	1		\|a Mohammad, Hassan \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Computational and applied mathematics \|d Berlin : Springer, 2003 \|g 39(2020), 2 vom: 18. Apr. \|w (DE-627)47617502X \|w (DE-600)2171678-X \|x 1807-0302 \|7 nnns
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912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
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912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
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912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
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912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
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912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
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912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
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912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
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912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
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matchkey_str	article:18070302:2020----::ntotepcrlrdetrjcinehdonnieroooe
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bklnumber	31.76 31.80
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allfields	10.1007/s40314-020-01151-5 doi (DE-627)SPR039444139 (SPR)s40314-020-01151-5-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Abubakar, Auwal Bala verfasserin aut A note on the spectral gradient projection method for nonlinear monotone equations with applications 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing. Nonlinear monotone equations (dpeaa)DE-He213 Spectral gradient method (dpeaa)DE-He213 Projection method (dpeaa)DE-He213 Global convergence (dpeaa)DE-He213 Compressive sensing (dpeaa)DE-He213 Kumam, Poom verfasserin aut Mohammad, Hassan verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 18. Apr. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:18 month:04 https://dx.doi.org/10.1007/s40314-020-01151-5 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_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 31.76 ASE 31.80 ASE AR 39 2020 2 18 04
spelling	10.1007/s40314-020-01151-5 doi (DE-627)SPR039444139 (SPR)s40314-020-01151-5-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Abubakar, Auwal Bala verfasserin aut A note on the spectral gradient projection method for nonlinear monotone equations with applications 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing. Nonlinear monotone equations (dpeaa)DE-He213 Spectral gradient method (dpeaa)DE-He213 Projection method (dpeaa)DE-He213 Global convergence (dpeaa)DE-He213 Compressive sensing (dpeaa)DE-He213 Kumam, Poom verfasserin aut Mohammad, Hassan verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 18. Apr. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:18 month:04 https://dx.doi.org/10.1007/s40314-020-01151-5 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_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 31.76 ASE 31.80 ASE AR 39 2020 2 18 04
allfields_unstemmed	10.1007/s40314-020-01151-5 doi (DE-627)SPR039444139 (SPR)s40314-020-01151-5-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Abubakar, Auwal Bala verfasserin aut A note on the spectral gradient projection method for nonlinear monotone equations with applications 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing. Nonlinear monotone equations (dpeaa)DE-He213 Spectral gradient method (dpeaa)DE-He213 Projection method (dpeaa)DE-He213 Global convergence (dpeaa)DE-He213 Compressive sensing (dpeaa)DE-He213 Kumam, Poom verfasserin aut Mohammad, Hassan verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 18. Apr. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:18 month:04 https://dx.doi.org/10.1007/s40314-020-01151-5 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_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 31.76 ASE 31.80 ASE AR 39 2020 2 18 04
allfieldsGer	10.1007/s40314-020-01151-5 doi (DE-627)SPR039444139 (SPR)s40314-020-01151-5-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Abubakar, Auwal Bala verfasserin aut A note on the spectral gradient projection method for nonlinear monotone equations with applications 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing. Nonlinear monotone equations (dpeaa)DE-He213 Spectral gradient method (dpeaa)DE-He213 Projection method (dpeaa)DE-He213 Global convergence (dpeaa)DE-He213 Compressive sensing (dpeaa)DE-He213 Kumam, Poom verfasserin aut Mohammad, Hassan verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 18. Apr. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:18 month:04 https://dx.doi.org/10.1007/s40314-020-01151-5 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_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 31.76 ASE 31.80 ASE AR 39 2020 2 18 04
allfieldsSound	10.1007/s40314-020-01151-5 doi (DE-627)SPR039444139 (SPR)s40314-020-01151-5-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl 31.80 bkl Abubakar, Auwal Bala verfasserin aut A note on the spectral gradient projection method for nonlinear monotone equations with applications 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing. Nonlinear monotone equations (dpeaa)DE-He213 Spectral gradient method (dpeaa)DE-He213 Projection method (dpeaa)DE-He213 Global convergence (dpeaa)DE-He213 Compressive sensing (dpeaa)DE-He213 Kumam, Poom verfasserin aut Mohammad, Hassan verfasserin aut Enthalten in Computational and applied mathematics Berlin : Springer, 2003 39(2020), 2 vom: 18. Apr. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:39 year:2020 number:2 day:18 month:04 https://dx.doi.org/10.1007/s40314-020-01151-5 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_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 31.76 ASE 31.80 ASE AR 39 2020 2 18 04
language	English
source	Enthalten in Computational and applied mathematics 39(2020), 2 vom: 18. Apr. volume:39 year:2020 number:2 day:18 month:04
sourceStr	Enthalten in Computational and applied mathematics 39(2020), 2 vom: 18. Apr. volume:39 year:2020 number:2 day:18 month:04
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Nonlinear monotone equations Spectral gradient method Projection method Global convergence Compressive sensing
dewey-raw	510
isfreeaccess_bool	false
container_title	Computational and applied mathematics
authorswithroles_txt_mv	Abubakar, Auwal Bala @@aut@@ Kumam, Poom @@aut@@ Mohammad, Hassan @@aut@@
publishDateDaySort_date	2020-04-18T00:00:00Z
hierarchy_top_id	47617502X
dewey-sort	3510
id	SPR039444139
language_de	englisch
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Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. 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author	Abubakar, Auwal Bala
spellingShingle	Abubakar, Auwal Bala ddc 510 bkl 31.76 bkl 31.80 misc Nonlinear monotone equations misc Spectral gradient method misc Projection method misc Global convergence misc Compressive sensing A note on the spectral gradient projection method for nonlinear monotone equations with applications
authorStr	Abubakar, Auwal Bala
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topic_title	510 ASE 31.76 bkl 31.80 bkl A note on the spectral gradient projection method for nonlinear monotone equations with applications Nonlinear monotone equations (dpeaa)DE-He213 Spectral gradient method (dpeaa)DE-He213 Projection method (dpeaa)DE-He213 Global convergence (dpeaa)DE-He213 Compressive sensing (dpeaa)DE-He213
topic	ddc 510 bkl 31.76 bkl 31.80 misc Nonlinear monotone equations misc Spectral gradient method misc Projection method misc Global convergence misc Compressive sensing
topic_unstemmed	ddc 510 bkl 31.76 bkl 31.80 misc Nonlinear monotone equations misc Spectral gradient method misc Projection method misc Global convergence misc Compressive sensing
topic_browse	ddc 510 bkl 31.76 bkl 31.80 misc Nonlinear monotone equations misc Spectral gradient method misc Projection method misc Global convergence misc Compressive sensing
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title	A note on the spectral gradient projection method for nonlinear monotone equations with applications
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title_full	A note on the spectral gradient projection method for nonlinear monotone equations with applications
author_sort	Abubakar, Auwal Bala
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author_browse	Abubakar, Auwal Bala Kumam, Poom Mohammad, Hassan
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author2-role	verfasserin
title_sort	note on the spectral gradient projection method for nonlinear monotone equations with applications
title_auth	A note on the spectral gradient projection method for nonlinear monotone equations with applications
abstract	Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing.
abstractGer	Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing.
abstract_unstemmed	Abstract In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing.
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title_short	A note on the spectral gradient projection method for nonlinear monotone equations with applications
url	https://dx.doi.org/10.1007/s40314-020-01151-5
remote_bool	true
author2	Kumam, Poom Mohammad, Hassan
author2Str	Kumam, Poom Mohammad, Hassan
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doi_str	10.1007/s40314-020-01151-5
up_date	2024-07-03T23:57:56.931Z
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A note on the spectral gradient projection method for nonlinear monotone equations with applications

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