Generalized forward–backward splitting with penalization for monotone inclusion problems
We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic co...
Uložené v:
| Vydané v: | Journal of global optimization Ročník 73; číslo 4; s. 825 - 847 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
15.04.2019
Springer Springer Nature B.V |
| Predmet: | |
| ISSN: | 0925-5001, 1573-2916 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems. |
|---|---|
| AbstractList | We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems. |
| Audience | Academic |
| Author | Petrot, Narin Nimana, Nimit |
| Author_xml | – sequence: 1 givenname: Nimit surname: Nimana fullname: Nimana, Nimit organization: Department of Mathematics, Faculty of Science, Khon Kaen University – sequence: 2 givenname: Narin orcidid: 0000-0001-6539-7107 surname: Petrot fullname: Petrot, Narin email: narinp@nu.ac.th organization: Department of Mathematics, Faculty of Science, Naresuan University, Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University |
| BookMark | eNp9UM1KAzEYDFLBtvoCnhY8b02yP8keS9EqFLzoxUtIs0lN3U3WJKXoyXfwDX0Ss11B8FBCSBhmvplvJmBkrJEAXCI4QxCSa48grWgKUbyQZDAtTsAYFSRLcYXKERjDChdpASE6AxPvtxDCihZ4DJ6X0kjHG_0h60RZt-eu_v78WnPx2n8T3zU6BG02yV6Hl6STpufyoK3p6UlrjQ0xS6KNaHa-hztn141s_Tk4Vbzx8uL3nYKn25vHxV26eljeL-arVGQFDSmCCtOyRFjmtOSSc07xmiqUYyUiQkpV1TnBElWiJLhWucJcxfw0w5jKrM6m4GqYG43fdtIHtrU7F3N6hhGlFJUFKSJrNrA2vJFMG2WD4yKeWrZaxA2UjvicIJrjnGRVFOBBIJz13knFOqdb7t4ZgqwvnQ2ls1g6O5TOehf6TyR0OLQV3XRzXJoNUh99zEa6vzWOqH4AAFWaZw |
| CitedBy_id | crossref_primary_10_1080_10556788_2018_1556660 crossref_primary_10_3390_su14127511 crossref_primary_10_1080_02331934_2020_1846188 |
| Cites_doi | 10.1080/00401706.1970.10488634 10.1007/s10957-011-9936-x 10.1137/130942954 10.1137/110820300 10.1137/15M1046095 10.1137/15M1018253 10.1007/s10013-017-0256-9 10.1137/120872802 10.1007/s11075-015-0007-5 10.1016/j.jde.2009.06.014 10.1007/BF03007664 10.1007/s10444-011-9254-8 10.1007/s10957-013-0296-6 10.1007/s11228-011-0191-y 10.1016/0022-247X(79)90234-8 10.1007/978-1-4419-9467-7 10.1007/s10107-016-1030-6 10.1080/02331934.2016.1181759 10.1137/140957639 10.1007/s10957-014-0700-x 10.1111/j.1467-9868.2005.00503.x 10.1137/100789464 10.1007/s11590-017-1158-1 10.1137/16M1080173 10.1142/5021 10.1137/140980910 10.1007/s11228-014-0274-7 10.1016/j.compbiolchem.2012.12.008 10.1007/s10013-013-0050-2 10.1111/j.2517-6161.1996.tb02080.x |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2018 COPYRIGHT 2019 Springer Journal of Global Optimization is a copyright of Springer, (2018). All Rights Reserved. |
| Copyright_xml | – notice: Springer Science+Business Media, LLC, part of Springer Nature 2018 – notice: COPYRIGHT 2019 Springer – notice: Journal of Global Optimization is a copyright of Springer, (2018). All Rights Reserved. |
| DBID | AAYXX CITATION 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- L.- L6V L7M L~C L~D M0C M0N M2O M2P M7S MBDVC P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1007/s10898-018-00730-5 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Research Library (Alumni) ProQuest Materials Science & Engineering ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Business Premium Collection Technology Collection ProQuest One ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student ProQuest Research Library SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Research Library Science Database Engineering Database Research Library (Corporate) ProQuest advanced technologies & aerospace journals ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business (UW System Shared) ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete ProQuest One Applied & Life Sciences ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Central Korea ProQuest Research Library Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | ProQuest Business Collection (Alumni Edition) |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics Sciences (General) Computer Science |
| EISSN | 1573-2916 |
| EndPage | 847 |
| ExternalDocumentID | A718424739 10_1007_s10898_018_00730_5 |
| GrantInformation_xml | – fundername: Thailand Research Fund grantid: RSA5880028 funderid: http://dx.doi.org/10.13039/501100004396 |
| GroupedDBID | -52 -57 -5G -BR -EM -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 203 29K 2J2 2JN 2JY 2KG 2LR 2~H 30V 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABUWG ABWNU ABXPI ACAOD ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYQZM AZFZN AZQEC B-. BA0 BAPOH BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CCPQU CS3 CSCUP D-I DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GUQSH GXS HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITC ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV L6V LAK LLZTM M0C M0N M2O M2P M4Y M7S MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P2P P62 P9M PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S27 S3B SAP SBE SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z5O Z7R Z7X Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8T Z8U Z8W Z92 ZMTXR ~EX -Y2 1SB 2.D 28- 2P1 2VQ 5QI AAPKM AARHV AAYTO AAYXX ABBRH ABDBE ABFSG ABQSL ABRTQ ABULA ACBXY ACSTC ADHKG AEBTG AEFIE AEKMD AEZWR AFDZB AFEXP AFFHD AFGCZ AFHIU AFOHR AGGDS AGQPQ AHPBZ AHWEU AI. AIXLP AJBLW AMVHM ATHPR AYFIA BBWZM CAG CITATION COF H13 KOW N2Q NDZJH O9- OVD PHGZM PHGZT PQGLB R4E RNI RZC RZE RZK S1Z S26 S28 SCLPG T16 TEORI VH1 ZWQNP ZY4 3V. 7SC 7XB 8AL 8FD 8FK JQ2 L.- L7M L~C L~D MBDVC PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c358t-10f286612e486aeaaa82b8f142fc48676f9d472e19c672df4f2af00083228e3d3 |
| IEDL.DBID | K7- |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000462013800007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0925-5001 |
| IngestDate | Tue Nov 04 22:33:07 EST 2025 Sat Nov 29 10:09:48 EST 2025 Tue Nov 18 21:58:25 EST 2025 Sat Nov 29 01:59:35 EST 2025 Fri Feb 21 02:42:28 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Monotone inclusion 65K05 90C25 65K10 Monotone operator Hierarchical optimization 47H05 Forward–backward algorithm |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c358t-10f286612e486aeaaa82b8f142fc48676f9d472e19c672df4f2af00083228e3d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-6539-7107 |
| PQID | 2188816575 |
| PQPubID | 29930 |
| PageCount | 23 |
| ParticipantIDs | proquest_journals_2188816575 gale_infotracacademiconefile_A718424739 crossref_primary_10_1007_s10898_018_00730_5 crossref_citationtrail_10_1007_s10898_018_00730_5 springer_journals_10_1007_s10898_018_00730_5 |
| PublicationCentury | 2000 |
| PublicationDate | 20190415 |
| PublicationDateYYYYMMDD | 2019-04-15 |
| PublicationDate_xml | – month: 4 year: 2019 text: 20190415 day: 15 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Dordrecht |
| PublicationSubtitle | An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering |
| PublicationTitle | Journal of global optimization |
| PublicationTitleAbbrev | J Glob Optim |
| PublicationYear | 2019 |
| Publisher | Springer US Springer Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer – name: Springer Nature B.V |
| References | Bauschke, Combettes (CR7) 2011 Boţ, Csetnek (CR11) 2016; 71 Hoerl, Kennard (CR20) 1970; 12 Raguet, Landrieu (CR29) 2015; 8 Zou, Hastie (CR35) 2005; 67 CR19 Passty (CR25) 1979; 72 CR15 Noun, Peypouquet (CR23) 2013; 158 Boţ, Csetnek (CR9) 2014; 42 Boţ, Csetnek (CR12) 2017; 66 Czarnecki, Noun, Peypouquet (CR18) 2016; 23 Schmidt, Le Roux, Bach (CR30) 2017; 162 Zălinescu (CR34) 2002 Attouch, Czarnecki (CR1) 2010; 248 Attouch, Peypouquet (CR4) 2016; 26 Mairal (CR22) 2015; 25 Boţ, Csetnek (CR10) 2014; 22 Tibshirani (CR33) 1996; 58 Attouch, Czarnecki, Peypouquet (CR2) 2011; 21 Shalev-Schwartz, Zhang (CR32) 2013; 14 Chen, Ma, Yang (CR16) 2015; 25 Baillon, Haddad (CR5) 1977; 26 Ochs, Chen, Brox, Pock (CR24) 2014; 7 Combettes, Pesquet (CR17) 2012; 20 Huang, Gong, Yang, He (CR21) 2013; 43 Polyak (CR27) 1987 Bottou, Curtis, Nocedal (CR8) 2018; 60 Vũ (CR31) 2013; 38 Boţ, Csetnek, Nimana (CR14) 2018; 46 Attouch, Czarnecki, Peypouquet (CR3) 2011; 21 Banert, Boţ (CR6) 2015; 166 Peypouquet (CR26) 2012; 153 Boţ, Csetnek, Nimana (CR13) 2018; 12 Raguet, Fadili, Peyré (CR28) 2013; 6 J-B Baillon (730_CR5) 1977; 26 J Peypouquet (730_CR26) 2012; 153 H Attouch (730_CR3) 2011; 21 GB Passty (730_CR25) 1979; 72 RI Boţ (730_CR11) 2016; 71 J Mairal (730_CR22) 2015; 25 H Raguet (730_CR29) 2015; 8 S Banert (730_CR6) 2015; 166 RI Boţ (730_CR14) 2018; 46 T Huang (730_CR21) 2013; 43 N Noun (730_CR23) 2013; 158 H Attouch (730_CR4) 2016; 26 BT Polyak (730_CR27) 1987 S Shalev-Schwartz (730_CR32) 2013; 14 730_CR15 C Zălinescu (730_CR34) 2002 730_CR19 L Bottou (730_CR8) 2018; 60 P Ochs (730_CR24) 2014; 7 RI Boţ (730_CR13) 2018; 12 PL Combettes (730_CR17) 2012; 20 HH Bauschke (730_CR7) 2011 RI Boţ (730_CR9) 2014; 42 M Schmidt (730_CR30) 2017; 162 C Chen (730_CR16) 2015; 25 AE Hoerl (730_CR20) 1970; 12 H Attouch (730_CR2) 2011; 21 M-O Czarnecki (730_CR18) 2016; 23 BC Vũ (730_CR31) 2013; 38 R Tibshirani (730_CR33) 1996; 58 RI Boţ (730_CR12) 2017; 66 H Attouch (730_CR1) 2010; 248 RI Boţ (730_CR10) 2014; 22 H Raguet (730_CR28) 2013; 6 H Zou (730_CR35) 2005; 67 |
| References_xml | – volume: 12 start-page: 55 year: 1970 end-page: 67 ident: CR20 article-title: Ridge regression: biased estimation for nonorthogonal problems publication-title: Technometrics doi: 10.1080/00401706.1970.10488634 – volume: 153 start-page: 123 issue: 1 year: 2012 end-page: 138 ident: CR26 article-title: Coupling the gradient method with a general exterior penalization scheme for convex minimization publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9936-x – volume: 7 start-page: 1388 issue: 2 year: 2014 end-page: 1419 ident: CR24 article-title: iPiano: inertial proximal algorithm for non-convex optimization publication-title: SIAM J. Imaging Sci. doi: 10.1137/130942954 – volume: 21 start-page: 1251 issue: 4 year: 2011 end-page: 1274 ident: CR3 article-title: Coupling forward–backward with penalty schemes and parallel splitting for constrained variational inequalities publication-title: SIAM J. Optim. doi: 10.1137/110820300 – volume: 26 start-page: 1824 year: 2016 end-page: 1834 ident: CR4 article-title: The rate of convergence of Nesterov’s accelerated forward–backward method is actually faster than publication-title: SIAM J. Optim. doi: 10.1137/15M1046095 – volume: 8 start-page: 2706 year: 2015 end-page: 2739 ident: CR29 article-title: Preconditioning of a generalized forward–backward splitting and application to optimization on graphs publication-title: SIAM J. Imaging Sci. doi: 10.1137/15M1018253 – volume: 46 start-page: 53 issue: 1 year: 2018 end-page: 71 ident: CR14 article-title: An inertial proximal-gradient penalization scheme for constrained convex optimization problems publication-title: Vietnam J. Math. doi: 10.1007/s10013-017-0256-9 – volume: 6 start-page: 1199 year: 2013 end-page: 1226 ident: CR28 article-title: A generalized forward–backward splitting: SIAM publication-title: J. Imaging Sci. doi: 10.1137/120872802 – volume: 71 start-page: 519 year: 2016 end-page: 540 ident: CR11 article-title: An inertial forward–backward–forward primal–dual splitting algorithm for solving monotone inclusion problems publication-title: Numer. Algorithms doi: 10.1007/s11075-015-0007-5 – volume: 248 start-page: 1315 issue: 6 year: 2010 end-page: 1344 ident: CR1 article-title: Asymptotic behavior of coupled dynamical systems with multiscale aspects publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2009.06.014 – volume: 26 start-page: 137 year: 1977 end-page: 150 ident: CR5 article-title: Quelques propriétés des opérateurs angle-bornés et -cycliquement monotones publication-title: Israel J. Math. doi: 10.1007/BF03007664 – volume: 38 start-page: 667 year: 2013 end-page: 681 ident: CR31 article-title: A splitting algorithm for dual monotone inclusions involving cocoercive operators publication-title: Adv. Comput. Math. doi: 10.1007/s10444-011-9254-8 – volume: 158 start-page: 787 issue: 3 year: 2013 end-page: 795 ident: CR23 article-title: Forward–backward penalty scheme for constrained convex minimization without inf-compactness publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0296-6 – volume: 14 start-page: 567 year: 2013 end-page: 599 ident: CR32 article-title: Stochastic dual coordinate ascent methods for regularized loss minimization publication-title: J. Mach. Learn. Res. – volume: 58 start-page: 267 year: 1996 end-page: 288 ident: CR33 article-title: Regression shrinkage and selection via the lasso publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. – volume: 20 start-page: 307 year: 2012 end-page: 330 ident: CR17 article-title: Primal–dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-011-0191-y – volume: 72 start-page: 383 year: 1979 end-page: 390 ident: CR25 article-title: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(79)90234-8 – year: 2011 ident: CR7 publication-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces doi: 10.1007/978-1-4419-9467-7 – volume: 23 start-page: 531 year: 2016 end-page: 565 ident: CR18 article-title: Splitting forward–backward penalty scheme for constrained variational problems publication-title: J. Convex Anal. – volume: 162 start-page: 83 issue: 1 year: 2017 end-page: 112 ident: CR30 article-title: Minimizing finite sums with the stochastic average gradient publication-title: Math. Program. doi: 10.1007/s10107-016-1030-6 – volume: 66 start-page: 965 year: 2017 end-page: 982 ident: CR12 article-title: Penalty schemes with inertial effects for monotone inclusion problems publication-title: Optimization doi: 10.1080/02331934.2016.1181759 – ident: CR19 – volume: 25 start-page: 829 issue: 2 year: 2015 end-page: 855 ident: CR22 article-title: Incremental majorization–minimization optimization with application to large-scale machine learning publication-title: SIAM J. Optim. doi: 10.1137/140957639 – volume: 166 start-page: 930 issue: 3 year: 2015 end-page: 948 ident: CR6 article-title: Backward penalty schemes for monotone inclusion problems publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-014-0700-x – volume: 67 start-page: 301 year: 2005 end-page: 320 ident: CR35 article-title: Regularization and variable selection via the elastic net publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. doi: 10.1111/j.1467-9868.2005.00503.x – volume: 21 start-page: 149 issue: 1 year: 2011 end-page: 173 ident: CR2 article-title: Prox-penalization and splitting methods for constrained variational problems publication-title: SIAM J. Optim. doi: 10.1137/100789464 – ident: CR15 – volume: 12 start-page: 17 issue: 1 year: 2018 end-page: 33 ident: CR13 article-title: Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data publication-title: Optim. Lett. doi: 10.1007/s11590-017-1158-1 – volume: 60 start-page: 223 issue: 2 year: 2018 end-page: 311 ident: CR8 article-title: Optimization methods for large-scale machine learning publication-title: SIAM Rev. doi: 10.1137/16M1080173 – year: 2002 ident: CR34 publication-title: Convex Analysis in General Vector Spaces doi: 10.1142/5021 – volume: 25 start-page: 2120 issue: 4 year: 2015 end-page: 2142 ident: CR16 article-title: A general inertial proximal point algorithm for mixed variational inequality problem publication-title: SIAM J. Optim. doi: 10.1137/140980910 – volume: 22 start-page: 313 year: 2014 end-page: 331 ident: CR10 article-title: Forward–backward and Tseng’s type penalty schemes for monotone inclusion problems publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-014-0274-7 – volume: 43 start-page: 46 year: 2013 end-page: 54 ident: CR21 article-title: ProteinLasso: a Lasso regression approach to protein inference problem in shotgun proteomics publication-title: Comp. Biol. Chem. doi: 10.1016/j.compbiolchem.2012.12.008 – year: 1987 ident: CR27 publication-title: Introduction to Optimization (Translated from the Russian). Translations Series in Mathematics and Engineering – volume: 42 start-page: 451 issue: 4 year: 2014 end-page: 465 ident: CR9 article-title: A Tseng’s type penalty scheme for solving inclusion problems involving linearly composed and parallel-sum type monotone operators publication-title: Vietnam J. Math. doi: 10.1007/s10013-013-0050-2 – volume: 7 start-page: 1388 issue: 2 year: 2014 ident: 730_CR24 publication-title: SIAM J. Imaging Sci. doi: 10.1137/130942954 – volume: 6 start-page: 1199 year: 2013 ident: 730_CR28 publication-title: J. Imaging Sci. doi: 10.1137/120872802 – volume: 26 start-page: 137 year: 1977 ident: 730_CR5 publication-title: Israel J. Math. doi: 10.1007/BF03007664 – volume: 38 start-page: 667 year: 2013 ident: 730_CR31 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-011-9254-8 – volume: 21 start-page: 149 issue: 1 year: 2011 ident: 730_CR2 publication-title: SIAM J. Optim. doi: 10.1137/100789464 – volume: 22 start-page: 313 year: 2014 ident: 730_CR10 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-014-0274-7 – volume-title: Convex Analysis in General Vector Spaces year: 2002 ident: 730_CR34 doi: 10.1142/5021 – volume: 46 start-page: 53 issue: 1 year: 2018 ident: 730_CR14 publication-title: Vietnam J. Math. doi: 10.1007/s10013-017-0256-9 – volume: 23 start-page: 531 year: 2016 ident: 730_CR18 publication-title: J. Convex Anal. – volume: 21 start-page: 1251 issue: 4 year: 2011 ident: 730_CR3 publication-title: SIAM J. Optim. doi: 10.1137/110820300 – volume: 60 start-page: 223 issue: 2 year: 2018 ident: 730_CR8 publication-title: SIAM Rev. doi: 10.1137/16M1080173 – volume: 25 start-page: 2120 issue: 4 year: 2015 ident: 730_CR16 publication-title: SIAM J. Optim. doi: 10.1137/140980910 – volume: 43 start-page: 46 year: 2013 ident: 730_CR21 publication-title: Comp. Biol. Chem. doi: 10.1016/j.compbiolchem.2012.12.008 – volume: 158 start-page: 787 issue: 3 year: 2013 ident: 730_CR23 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0296-6 – volume: 58 start-page: 267 year: 1996 ident: 730_CR33 publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. doi: 10.1111/j.2517-6161.1996.tb02080.x – volume-title: Introduction to Optimization (Translated from the Russian). Translations Series in Mathematics and Engineering year: 1987 ident: 730_CR27 – volume: 72 start-page: 383 year: 1979 ident: 730_CR25 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(79)90234-8 – volume: 25 start-page: 829 issue: 2 year: 2015 ident: 730_CR22 publication-title: SIAM J. Optim. doi: 10.1137/140957639 – volume: 153 start-page: 123 issue: 1 year: 2012 ident: 730_CR26 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9936-x – volume: 67 start-page: 301 year: 2005 ident: 730_CR35 publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. doi: 10.1111/j.1467-9868.2005.00503.x – volume: 42 start-page: 451 issue: 4 year: 2014 ident: 730_CR9 publication-title: Vietnam J. Math. doi: 10.1007/s10013-013-0050-2 – volume: 71 start-page: 519 year: 2016 ident: 730_CR11 publication-title: Numer. Algorithms doi: 10.1007/s11075-015-0007-5 – volume: 162 start-page: 83 issue: 1 year: 2017 ident: 730_CR30 publication-title: Math. Program. doi: 10.1007/s10107-016-1030-6 – volume-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces year: 2011 ident: 730_CR7 doi: 10.1007/978-1-4419-9467-7 – volume: 12 start-page: 17 issue: 1 year: 2018 ident: 730_CR13 publication-title: Optim. Lett. doi: 10.1007/s11590-017-1158-1 – ident: 730_CR15 – volume: 14 start-page: 567 year: 2013 ident: 730_CR32 publication-title: J. Mach. Learn. Res. – ident: 730_CR19 – volume: 8 start-page: 2706 year: 2015 ident: 730_CR29 publication-title: SIAM J. Imaging Sci. doi: 10.1137/15M1018253 – volume: 166 start-page: 930 issue: 3 year: 2015 ident: 730_CR6 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-014-0700-x – volume: 12 start-page: 55 year: 1970 ident: 730_CR20 publication-title: Technometrics doi: 10.1080/00401706.1970.10488634 – volume: 26 start-page: 1824 year: 2016 ident: 730_CR4 publication-title: SIAM J. Optim. doi: 10.1137/15M1046095 – volume: 248 start-page: 1315 issue: 6 year: 2010 ident: 730_CR1 publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2009.06.014 – volume: 20 start-page: 307 year: 2012 ident: 730_CR17 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-011-0191-y – volume: 66 start-page: 965 year: 2017 ident: 730_CR12 publication-title: Optimization doi: 10.1080/02331934.2016.1181759 |
| SSID | ssj0009852 |
| Score | 2.2361019 |
| Snippet | We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of... We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of... |
| SourceID | proquest gale crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 825 |
| SubjectTerms | Computer Science Convergence Mathematical analysis Mathematics Mathematics and Statistics Operations Research/Decision Theory Operators (mathematics) Optimization Real Functions Splitting |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwEB6VhQM9UHahauhS-YBUEI20cZzEPq4qKg6lQvShiosVO7a0UrWtmt0eeuI_8A_5Jcx4nd3yqkRveThjy55XPJ5vAN5YV_vSSpUqk0n8QfGj1PiySa3hhSlVLl3Y0D87rI6O5Pm5-hyTwtrutHsXkgya-k6ym6R0MCRJ4aVRWjyCx2juJInjl-OzFdSuDHV2RooXaYFaOKbK_J3GL-bod6X8R3Q0GJ2DjYcN9zk8i04mGy-4og9rbjqAja6AA4vyPID1O2iEePdpCeHaDqAfW7XsbYSmfvcCvsbLya1rGLq7dOT2x7fvhjYB8ZK16NKGg9SM9nfZlSM3f5HoSc0Z8vwloX-zydRezGmjjsWKNu1LOD34cLL_MY3VGVKbF3KG-ttzidadOyHL2tV1LbmRPhPcW4LxK71qRMVdpmxZ8cYLz2sfXD7OpcubfBN6U-xxC1jhfJMbJQxSFEKVRlT4yNfO5wZ5Jk8g6xZJ2whdThU0LvQKdJlmW-Ns6zDbukjg_fKbqwVwx72td2ntNUk1UrZ1TE7A8RE-lh6jCRdcVLlKYNixh47i3mr0k6TMKIaVwF7HDqvX_-731f8134an6LCFaFZWDKE3u5671_DE3swm7fVOEIOfcfkCcw priority: 102 providerName: Springer Nature |
| Title | Generalized forward–backward splitting with penalization for monotone inclusion problems |
| URI | https://link.springer.com/article/10.1007/s10898-018-00730-5 https://www.proquest.com/docview/2188816575 |
| Volume | 73 |
| WOSCitedRecordID | wos000462013800007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: Springer LINK customDbUrl: eissn: 1573-2916 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NbhQxDLZoywEO0BYQC2WVAxIgiNjJJDPJCZWqFRKwrFoopZdokkmklart0tly4MQ78IY8CXY22-VH9MLFGs1PEsmO7bHjzwAPfWhi5bXhxhUaf1DigLtYtdw7oVxlSh1SQP_wTT0c6qMjM8oBty4fq1zoxKSo21NPMfLnaIq0LihN8GL6mVPXKMqu5hYaK7BWCFGQnL-u-RJ0V6eOOwMjFFeoj3PRTC6d01RchgukZNWAq98M05_q-a88aTI_ezf_d-HrcCM7nmx7LikbcCVMNuH6L3CEm7CRN3rHHmc06ie34Dhfjr-GlqGHS6dsf3z77ijuh5esQy82nZ1mFNJl00Ce_by2k15nOP0pAX6z8cSfnFNsjuUmNt1t-LC3-37nFc8NGbgvlZ6hyo5Co0EXQeqqCU3TaOF0LKSInpD7qmhaWYtQGF_Voo0yiiYmL08IHcq2vAOrE5zxLjAVYls6Ix2OKKWpnKzxVmxCLB2KSdmDYsEN6zNaOTXNOLFLnGXioEUO2sRBq3rw9OKb6Ryr49K3HxGTLW1kHNk3uR4B10eQWHYbrbYUsi5ND7YWnLV5h3d2ydYePFvIxvLxv-e9d_lo9-Ea-mQpYVWoLVidnZ2HB3DVf5mNu7M-rNQfP_Vh7eXucLTfT9KO9O1gh6h4l-iIaH2AdKSOke4fHP4EDcoJ0A |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwEB6VggQcWlpAbH_ABxAgiNg4TmIfqqoqVK26rDgUVPViYseWVqq2S7Nt1Z76DrwHD8WTMON1WH5Ebz1wi_LjJPbnmfGM5xuAp9ZVvrBSJcqkEhcovpsYX9SJNTw3hcqkCw79T72y35f7--rDDHxrc2FoW2UrE4Ogro8s-cjfoCqSMqUwwfroS0JVoyi62pbQmMBi152f4ZKtWdt5i-P7jPOtd3ub20msKpDYLJdjlDueS9RK3AlZVK6qKsmN9Kng3hL9XOFVLUruUmWLktdeeF75YKpwLl1WZ9juDbgpBE4H2irY3ZyS_MpQ4aereJ7kKP9jkk5M1ZOUzIYdQsGxbpL_pgj_VAd_xWWDutua_9866h7MRcOabUxmwgLMuOEi3P2FbnERFqIga9iLyLb98j4cxMPBhasZWvC0i_j75VdDfk08ZA1a6WFvOCOXNRs5WrlMclfpdoa_e0SE5mwwtIcn5HtksUhP8wA-XssfP4TZIb7xEbDc-TozShhsUQhVGFHiKV85nxmcBlkH0nb0tY1s7FQU5FBPeaQJMRoRowNidN6BVz-fGU24SK68-zmBSpOgwpZtFfMt8PuI8ktvoFUiuCgz1YGVFkk6SrBGT2HUgdctFqeX__3epatbewK3t_fe93Rvp7-7DHfQ_gzBuTRfgdnx8YlbhVv2dDxojh-HucXg83Vj9AdlQF0T |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LbtQwFL0qBaGyAFpAHSjgBQgQRJ04dmIvEKooI6pWo1kAqrpxY8eWRqqmQzMFwYp_4G_4HL6Eez0Ow0N01wW7KA_ndXyfvucCPHC-DqVTOtM2V-ighH5mQ9lkznJpS10oHwP67_aq4VDt7-vREnzramFoWWUnE6Ogbo4dxcg3URUplVOaYDOkZRGj7cGL6fuMOkhRprVrpzGHyK7_9BHdt_b5zjb-64ecD169efk6Sx0GMldINUMZFLhCDcW9UGXt67pW3KqQCx4cUdGVQTei4j7Xrqx4E0TgdYhmC-fKF02B416AixX6mOT4jeTBgvBXxW4_fc1lJlEXpIKdVLanqLANPw4lyvqZ_E0p_qka_srRRtU3uPY_f7TrcDUZ3GxrPkNWYclP1uDKLzSMa7CaBFzLHicW7ic34CBtjj_7hqFlT6uLv3_5aineiZusRes9rhlnFMpmU08ezbymlU5n-LrHRHTOxhN3dEoxSZaa97Q34e25vPEtWJ7gHdeBSR-awmphcUQhdGlFhbtC7UNhcXoUPcg7JBiXWNqpWciRWfBLE3oMosdE9BjZg6c_r5nOOUrOPPsRAcyQAMORXZ3qMPD5iArMbKG1IrioCt2DjQ5VJkm21iwg1YNnHS4Xh_9939tnj3YfLiM0zd7OcPcOrKBZGnN2udyA5dnJqb8Ll9yH2bg9uRenGYPD84boD4_9ZiQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Generalized+forward%E2%80%93backward+splitting+with+penalization+for+monotone+inclusion+problems&rft.jtitle=Journal+of+global+optimization&rft.au=Nimana%2C+Nimit&rft.au=Petrot%2C+Narin&rft.date=2019-04-15&rft.pub=Springer+Nature+B.V&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=73&rft.issue=4&rft.spage=825&rft.epage=847&rft_id=info:doi/10.1007%2Fs10898-018-00730-5&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-5001&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-5001&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-5001&client=summon |