Biorthogonal Greedy Algorithms in convex optimization
The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being employed to construct sparse minimizers for convex functions with respect to given sets of elements. In this paper we propose a unified way of an...
Gespeichert in:
| Veröffentlicht in: | Applied and computational harmonic analysis Jg. 60; S. 489 - 511 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier Inc
01.09.2022
|
| Schlagworte: | |
| ISSN: | 1063-5203, 1096-603X |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being employed to construct sparse minimizers for convex functions with respect to given sets of elements. In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms for the minimization of convex functions on Banach spaces. Specifically, we define the class of Weak Biorthogonal Greedy Algorithms for convex optimization that contains a wide range of greedy algorithms. We analyze the introduced class of algorithms and establish the properties of convergence, rate of convergence, and numerical stability, which is understood in the sense that the steps of the algorithm are allowed to be performed not precisely but with controlled computational inaccuracies. We show that the following well-known algorithms for convex optimization — the Weak Chebyshev Greedy Algorithm (co) and the Weak Greedy Algorithm with Free Relaxation (co) — belong to this class, and introduce a new algorithm — the Rescaled Weak Relaxed Greedy Algorithm (co). Presented numerical experiments demonstrate the practical performance of the aforementioned greedy algorithms in the setting of convex minimization as compared to optimization with regularization, which is the conventional approach of constructing sparse minimizers. |
|---|---|
| AbstractList | The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being employed to construct sparse minimizers for convex functions with respect to given sets of elements. In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms for the minimization of convex functions on Banach spaces. Specifically, we define the class of Weak Biorthogonal Greedy Algorithms for convex optimization that contains a wide range of greedy algorithms. We analyze the introduced class of algorithms and establish the properties of convergence, rate of convergence, and numerical stability, which is understood in the sense that the steps of the algorithm are allowed to be performed not precisely but with controlled computational inaccuracies. We show that the following well-known algorithms for convex optimization — the Weak Chebyshev Greedy Algorithm (co) and the Weak Greedy Algorithm with Free Relaxation (co) — belong to this class, and introduce a new algorithm — the Rescaled Weak Relaxed Greedy Algorithm (co). Presented numerical experiments demonstrate the practical performance of the aforementioned greedy algorithms in the setting of convex minimization as compared to optimization with regularization, which is the conventional approach of constructing sparse minimizers. |
| Author | Dereventsov, A.V. Temlyakov, V.N. |
| Author_xml | – sequence: 1 givenname: A.V. orcidid: 0000-0002-7095-8236 surname: Dereventsov fullname: Dereventsov, A.V. email: dereventsov@gmail.com organization: Oak Ridge National Laboratory, United States of America – sequence: 2 givenname: V.N. surname: Temlyakov fullname: Temlyakov, V.N. email: temlyakovv@gmail.com organization: University of South Carolina, United States of America |
| BookMark | eNp9j7FOwzAURS1UJNrCDzDlBxKe7dhpJJZSQUGqxAISm-XYL62rNK4cq6J8PUnLxNDp3eGdq3smZNT6Fgm5p5BRoPJhm2mz0RkDxjIQGQC9ImMKpUwl8K_RkCVPBQN-QyZdt-0faC7KMRFPzoe48Wvf6iZZBkR7TObN2gcXN7sucW1ifHvA78Tvo9u5Hx2db2_Jda2bDu_-7pR8vjx_LF7T1fvybTFfpYYDxBSRWyqoNlWd24IzlhfG8twgrUqwUGqDUrJKzgQtSl5DKUwNWpra5hR4UfEpmZ17TfBdF7BWxsXTghi0axQFNeirrRr01aCvQKjerkfZP3Qf3E6H42Xo8QxhL3VwGFRnHLYGrQtoorLeXcJ_Aau0dlk |
| CitedBy_id | crossref_primary_10_1063_5_0222940 crossref_primary_10_3390_axioms14060446 crossref_primary_10_4213_rm10186 crossref_primary_10_1177_09544100251343664 crossref_primary_10_1007_s10915_025_03050_5 crossref_primary_10_1142_S0219649224500692 crossref_primary_10_3103_S0027132225700214 crossref_primary_10_4213_rm10186e crossref_primary_10_1016_j_cie_2024_110482 crossref_primary_10_3390_math11112559 |
| Cites_doi | 10.1109/TSP.2009.2025088 10.1109/TIT.2002.808136 10.1023/A:1018917218956 10.1016/j.acha.2015.10.008 10.1016/j.jmaa.2015.12.006 10.1109/TSP.2007.916124 10.1007/s10208-015-9248-x 10.1145/1824777.1824783 10.1007/BF03024948 10.1017/S0962492900002816 10.1007/s10092-019-0311-x 10.1137/090759574 10.1090/S0002-9939-08-09630-5 10.1007/s10208-012-9135-7 10.1051/m2an/2011056 10.1134/S0081543814010180 10.1007/s00365-014-9272-0 10.1007/s00365-004-0565-6 10.1007/BF02678464 10.1023/A:1012255021470 10.1016/j.jfa.2019.108286 10.1109/JSTSP.2007.910281 10.1137/100795772 |
| ContentType | Journal Article |
| Copyright | 2022 Elsevier Inc. |
| Copyright_xml | – notice: 2022 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.acha.2022.05.001 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1096-603X |
| EndPage | 511 |
| ExternalDocumentID | 10_1016_j_acha_2022_05_001 S1063520322000410 |
| GroupedDBID | --K --M .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AASFE AAXUO ABAOU ABFNM ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADFGL ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CAG COF CS3 DM4 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HVGLF HZ~ IHE IXB J1W KOM LG5 M26 M41 MCRUF MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K WUQ XPP ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c300t-ee3d151acbf4d732247cd34ce1b90d09ace662b6851793f095cf0a6cfd41037b3 |
| ISICitedReferencesCount | 12 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000808576100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1063-5203 |
| IngestDate | Sat Nov 29 07:08:40 EST 2025 Tue Nov 18 22:38:12 EST 2025 Fri Feb 23 02:41:23 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Greedy algorithm Sparsity Biorthogonal Greedy Algorithm Banach space Convex optimization |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c300t-ee3d151acbf4d732247cd34ce1b90d09ace662b6851793f095cf0a6cfd41037b3 |
| ORCID | 0000-0002-7095-8236 |
| PageCount | 23 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_acha_2022_05_001 crossref_primary_10_1016_j_acha_2022_05_001 elsevier_sciencedirect_doi_10_1016_j_acha_2022_05_001 |
| PublicationCentury | 2000 |
| PublicationDate | September 2022 2022-09-00 |
| PublicationDateYYYYMMDD | 2022-09-01 |
| PublicationDate_xml | – month: 09 year: 2022 text: September 2022 |
| PublicationDecade | 2020 |
| PublicationTitle | Applied and computational harmonic analysis |
| PublicationYear | 2022 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Rozza, Huynh, Patera (br0260) 2007; 15 Blumensath, Davies (br0030) 2008; 56 Dereventsov (br0110) 2017 Nesterov (br0230) 2004 Chandrasekaran, Recht, Parrilo, Willsky (br0080) 2012; 12 Shalev-Shwartz, Srebro, Zhang (br0270) 2010; 20 Temlyakov (br0280) 2000; 12 Jaggi, Sulovský (br0220) 2010 Borwein, Guirao, Hájek, Vanderwerff (br0050) 2009; 137 Temlyakov (br0290) 2005; 21 Dereventsov, Webster (br0120) 2019 Jaggi (br0210) 2013 Dereventsov, Temlyakov (br0130) 2019; 277 Donahue, Darken, Gurvits, Sontag (br0160) 1997; 13 Temlyakov (br0330) 2016; 293 Clarkson (br0090) 2010; 6 Tewari, Ravikumar, Dhillon (br0340) 2011 DeVore (br0140) 1998; 7 Figueiredo, Nowak, Wright (br0170) 2007; 1 Temlyakov (br0310) 2015; 41 Temlyakov (br0320) 2014; 284 Petrova (br0250) 2016; 41 Zhang (br0350) 2003; 49 Beauzamy (br0010) 1982 Dereventsov (br0100) 2016; 436 Buffa, Maday, Patera, Prud'homme, Turinici (br0070) 2012; 46 Gao, Petrova (br0190) 2019; 56 Binev, Cohen, Dahmen, DeVore, Petrova, Wojtaszczyk (br0020) 2011; 43 Blumensath, Davies (br0040) 2009; 57 Temlyakov (br0300) 2011 Nguyen, Petrova (br0240) 2016 Boyd, Vandenberghe (br0060) 2004 DeVore, Temlyakov (br0150) 2016; 16 Gribonval, Nielsen (br0200) 2001; 14 Galatenko, Livshitz (br0180) 2003; 9 Shalev-Shwartz (10.1016/j.acha.2022.05.001_br0270) 2010; 20 Temlyakov (10.1016/j.acha.2022.05.001_br0320) 2014; 284 Chandrasekaran (10.1016/j.acha.2022.05.001_br0080) 2012; 12 DeVore (10.1016/j.acha.2022.05.001_br0150) 2016; 16 Rozza (10.1016/j.acha.2022.05.001_br0260) 2007; 15 Jaggi (10.1016/j.acha.2022.05.001_br0210) 2013 Clarkson (10.1016/j.acha.2022.05.001_br0090) 2010; 6 Temlyakov (10.1016/j.acha.2022.05.001_br0310) 2015; 41 Blumensath (10.1016/j.acha.2022.05.001_br0040) 2009; 57 Temlyakov (10.1016/j.acha.2022.05.001_br0330) 2016; 293 Gao (10.1016/j.acha.2022.05.001_br0190) 2019; 56 Galatenko (10.1016/j.acha.2022.05.001_br0180) 2003; 9 Jaggi (10.1016/j.acha.2022.05.001_br0220) 2010 Dereventsov (10.1016/j.acha.2022.05.001_br0120) Donahue (10.1016/j.acha.2022.05.001_br0160) 1997; 13 Buffa (10.1016/j.acha.2022.05.001_br0070) 2012; 46 Boyd (10.1016/j.acha.2022.05.001_br0060) 2004 Borwein (10.1016/j.acha.2022.05.001_br0050) 2009; 137 Figueiredo (10.1016/j.acha.2022.05.001_br0170) 2007; 1 Tewari (10.1016/j.acha.2022.05.001_br0340) 2011 Beauzamy (10.1016/j.acha.2022.05.001_br0010) 1982 Dereventsov (10.1016/j.acha.2022.05.001_br0100) 2016; 436 Gribonval (10.1016/j.acha.2022.05.001_br0200) 2001; 14 Temlyakov (10.1016/j.acha.2022.05.001_br0280) 2000; 12 Dereventsov (10.1016/j.acha.2022.05.001_br0130) 2019; 277 Nguyen (10.1016/j.acha.2022.05.001_br0240) 2016 Blumensath (10.1016/j.acha.2022.05.001_br0030) 2008; 56 DeVore (10.1016/j.acha.2022.05.001_br0140) 1998; 7 Temlyakov (10.1016/j.acha.2022.05.001_br0300) 2011 Zhang (10.1016/j.acha.2022.05.001_br0350) 2003; 49 Petrova (10.1016/j.acha.2022.05.001_br0250) 2016; 41 Temlyakov (10.1016/j.acha.2022.05.001_br0290) 2005; 21 Binev (10.1016/j.acha.2022.05.001_br0020) 2011; 43 Dereventsov (10.1016/j.acha.2022.05.001_br0110) 2017 Nesterov (10.1016/j.acha.2022.05.001_br0230) 2004 |
| References_xml | – volume: 16 start-page: 369 year: 2016 end-page: 394 ident: br0150 article-title: Convex optimization on Banach spaces publication-title: Found. Comput. Math. – volume: 1 start-page: 586 year: 2007 end-page: 597 ident: br0170 article-title: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems publication-title: IEEE J. Sel. Top. Signal Process. – year: 2011 ident: br0300 article-title: Greedy Approximation – volume: 15 year: 2007 ident: br0260 article-title: Reduced basis approximation and a posteriori error estimation for affinely parameterized elliptic coercive partial differential equations publication-title: Arch. Comput. Methods Eng. – volume: 21 start-page: 257 year: 2005 end-page: 292 ident: br0290 article-title: Greedy type algorithms in Banach spaces and applications publication-title: Constr. Approx. – volume: 43 start-page: 1457 year: 2011 end-page: 1472 ident: br0020 article-title: Convergence rates for greedy algorithms in reduced basis methods publication-title: SIAM J. Math. Anal. – volume: 41 start-page: 269 year: 2015 end-page: 296 ident: br0310 article-title: Greedy approximation in convex optimization publication-title: Constr. Approx. – year: 1982 ident: br0010 article-title: Introduction to Banach Spaces and Their Geometry – volume: 436 start-page: 288 year: 2016 end-page: 304 ident: br0100 article-title: On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces publication-title: J. Math. Anal. Appl. – start-page: 1 year: 2016 end-page: 18 ident: br0240 article-title: Greedy strategies for convex optimization publication-title: Calcolo – volume: 56 start-page: 2370 year: 2008 end-page: 2382 ident: br0030 article-title: Gradient pursuits publication-title: IEEE Trans. Signal Process. – volume: 137 start-page: 1081 year: 2009 end-page: 1091 ident: br0050 article-title: Uniformly convex functions on Banach spaces publication-title: Proc. Am. Math. Soc. – volume: 20 start-page: 2807 year: 2010 end-page: 2832 ident: br0270 article-title: Trading accuracy for sparsity in optimization problems with sparsity constrains publication-title: SIAM J. Optim. – start-page: 427 year: 2013 end-page: 435 ident: br0210 article-title: Revisiting Frank-Wolfe: projection-free sparse convex optimization publication-title: International Conference on Machine Learning, vol. 1 – volume: 7 start-page: 51 year: 1998 end-page: 150 ident: br0140 article-title: Nonlinear approximation publication-title: Acta Numer. – volume: 41 start-page: 852 year: 2016 end-page: 866 ident: br0250 article-title: Rescaled Pure Greedy Algorithm for Hilbert and Banach spaces publication-title: Appl. Comput. Harmon. Anal. – volume: 49 start-page: 682 year: 2003 end-page: 691 ident: br0350 article-title: Sequential greedy approximation for certain convex optimization problems publication-title: IEEE Trans. Inf. Theory – volume: 9 start-page: 43 year: 2003 end-page: 50 ident: br0180 article-title: On the convergence of approximate weak greedy algorithms publication-title: East J. Approx. – volume: 14 start-page: 361 year: 2001 end-page: 378 ident: br0200 article-title: Approximate weak greedy algorithms publication-title: Adv. Comput. Math. – volume: 284 start-page: 244 year: 2014 end-page: 262 ident: br0320 article-title: Greedy expansions in convex optimization publication-title: Proc. Steklov Inst. Math. – start-page: 882 year: 2011 end-page: 890 ident: br0340 article-title: Greedy algorithms for structurally constrained high dimensional problems publication-title: Adv. Neural Inf. Process. Syst. – volume: 56 year: 2019 ident: br0190 article-title: Rescaled Pure Greedy Algorithm for convex optimization publication-title: Calcolo – volume: 6 start-page: 63 year: 2010 ident: br0090 article-title: Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm publication-title: ACM Trans. Algorithms – year: 2019 ident: br0120 article-title: The Natural Greedy Algorithm for reduced bases in Banach spaces – volume: 12 start-page: 805 year: 2012 end-page: 849 ident: br0080 article-title: The convex geometry of linear inverse problems publication-title: Found. Comput. Math. – volume: 46 start-page: 595 year: 2012 end-page: 603 ident: br0070 article-title: A priori convergence of the greedy algorithm for the parametrized reduced basis method publication-title: ESAIM: Math. Model. Numer. Anal. – year: 2010 ident: br0220 article-title: A simple algorithm for nuclear norm regularized problems publication-title: International Conference on Machine Learning – volume: 12 start-page: 213 year: 2000 end-page: 227 ident: br0280 article-title: Weak Greedy Algorithms publication-title: Adv. Comput. Math. – year: 2004 ident: br0230 article-title: Introductory Lectures on Convex Optimization: A Basic Course – volume: 293 start-page: 333 year: 2016 end-page: 345 ident: br0330 article-title: Convergence and rate of convergence of some greedy algorithms in convex optimization publication-title: Tr. Mat. Inst. Steklova – volume: 13 start-page: 187 year: 1997 end-page: 220 ident: br0160 article-title: Rates of convex approximation in non-Hilbert spaces publication-title: Constr. Approx. – volume: 57 start-page: 4333 year: 2009 end-page: 4346 ident: br0040 article-title: Stagewise weak gradient pursuits publication-title: IEEE Trans. Signal Process. – volume: 277 year: 2019 ident: br0130 article-title: A unified way of analyzing some greedy algorithms publication-title: J. Funct. Anal. – year: 2004 ident: br0060 article-title: Convex Optimization – year: 2017 ident: br0110 article-title: Convergence and rate of convergence of approximate greedy-type algorithms – volume: 57 start-page: 4333 year: 2009 ident: 10.1016/j.acha.2022.05.001_br0040 article-title: Stagewise weak gradient pursuits publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2009.2025088 – volume: 49 start-page: 682 issue: 3 year: 2003 ident: 10.1016/j.acha.2022.05.001_br0350 article-title: Sequential greedy approximation for certain convex optimization problems publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2002.808136 – volume: 12 start-page: 213 issue: 2–3 year: 2000 ident: 10.1016/j.acha.2022.05.001_br0280 article-title: Weak Greedy Algorithms publication-title: Adv. Comput. Math. doi: 10.1023/A:1018917218956 – year: 1982 ident: 10.1016/j.acha.2022.05.001_br0010 – volume: 41 start-page: 852 year: 2016 ident: 10.1016/j.acha.2022.05.001_br0250 article-title: Rescaled Pure Greedy Algorithm for Hilbert and Banach spaces publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2015.10.008 – year: 2011 ident: 10.1016/j.acha.2022.05.001_br0300 – volume: 436 start-page: 288 issue: 1 year: 2016 ident: 10.1016/j.acha.2022.05.001_br0100 article-title: On the Approximate Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.12.006 – volume: 56 start-page: 2370 year: 2008 ident: 10.1016/j.acha.2022.05.001_br0030 article-title: Gradient pursuits publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2007.916124 – volume: 16 start-page: 369 year: 2016 ident: 10.1016/j.acha.2022.05.001_br0150 article-title: Convex optimization on Banach spaces publication-title: Found. Comput. Math. doi: 10.1007/s10208-015-9248-x – volume: 6 start-page: 63 issue: 4 year: 2010 ident: 10.1016/j.acha.2022.05.001_br0090 article-title: Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm publication-title: ACM Trans. Algorithms doi: 10.1145/1824777.1824783 – year: 2004 ident: 10.1016/j.acha.2022.05.001_br0230 – volume: 293 start-page: 333 year: 2016 ident: 10.1016/j.acha.2022.05.001_br0330 article-title: Convergence and rate of convergence of some greedy algorithms in convex optimization publication-title: Tr. Mat. Inst. Steklova – volume: 15 issue: 3 year: 2007 ident: 10.1016/j.acha.2022.05.001_br0260 article-title: Reduced basis approximation and a posteriori error estimation for affinely parameterized elliptic coercive partial differential equations publication-title: Arch. Comput. Methods Eng. doi: 10.1007/BF03024948 – year: 2017 ident: 10.1016/j.acha.2022.05.001_br0110 – volume: 7 start-page: 51 year: 1998 ident: 10.1016/j.acha.2022.05.001_br0140 article-title: Nonlinear approximation publication-title: Acta Numer. doi: 10.1017/S0962492900002816 – volume: 56 year: 2019 ident: 10.1016/j.acha.2022.05.001_br0190 article-title: Rescaled Pure Greedy Algorithm for convex optimization publication-title: Calcolo doi: 10.1007/s10092-019-0311-x – volume: 20 start-page: 2807 issue: 6 year: 2010 ident: 10.1016/j.acha.2022.05.001_br0270 article-title: Trading accuracy for sparsity in optimization problems with sparsity constrains publication-title: SIAM J. Optim. doi: 10.1137/090759574 – volume: 137 start-page: 1081 issue: 3 year: 2009 ident: 10.1016/j.acha.2022.05.001_br0050 article-title: Uniformly convex functions on Banach spaces publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-08-09630-5 – volume: 12 start-page: 805 issue: 6 year: 2012 ident: 10.1016/j.acha.2022.05.001_br0080 article-title: The convex geometry of linear inverse problems publication-title: Found. Comput. Math. doi: 10.1007/s10208-012-9135-7 – start-page: 1 year: 2016 ident: 10.1016/j.acha.2022.05.001_br0240 article-title: Greedy strategies for convex optimization publication-title: Calcolo – year: 2010 ident: 10.1016/j.acha.2022.05.001_br0220 article-title: A simple algorithm for nuclear norm regularized problems – volume: 46 start-page: 595 issue: 3 year: 2012 ident: 10.1016/j.acha.2022.05.001_br0070 article-title: A priori convergence of the greedy algorithm for the parametrized reduced basis method publication-title: ESAIM: Math. Model. Numer. Anal. doi: 10.1051/m2an/2011056 – volume: 9 start-page: 43 issue: 1 year: 2003 ident: 10.1016/j.acha.2022.05.001_br0180 article-title: On the convergence of approximate weak greedy algorithms publication-title: East J. Approx. – volume: 284 start-page: 244 year: 2014 ident: 10.1016/j.acha.2022.05.001_br0320 article-title: Greedy expansions in convex optimization publication-title: Proc. Steklov Inst. Math. doi: 10.1134/S0081543814010180 – volume: 41 start-page: 269 year: 2015 ident: 10.1016/j.acha.2022.05.001_br0310 article-title: Greedy approximation in convex optimization publication-title: Constr. Approx. doi: 10.1007/s00365-014-9272-0 – ident: 10.1016/j.acha.2022.05.001_br0120 – volume: 21 start-page: 257 year: 2005 ident: 10.1016/j.acha.2022.05.001_br0290 article-title: Greedy type algorithms in Banach spaces and applications publication-title: Constr. Approx. doi: 10.1007/s00365-004-0565-6 – start-page: 427 year: 2013 ident: 10.1016/j.acha.2022.05.001_br0210 article-title: Revisiting Frank-Wolfe: projection-free sparse convex optimization – volume: 13 start-page: 187 issue: 2 year: 1997 ident: 10.1016/j.acha.2022.05.001_br0160 article-title: Rates of convex approximation in non-Hilbert spaces publication-title: Constr. Approx. doi: 10.1007/BF02678464 – volume: 14 start-page: 361 year: 2001 ident: 10.1016/j.acha.2022.05.001_br0200 article-title: Approximate weak greedy algorithms publication-title: Adv. Comput. Math. doi: 10.1023/A:1012255021470 – volume: 277 issue: 12 year: 2019 ident: 10.1016/j.acha.2022.05.001_br0130 article-title: A unified way of analyzing some greedy algorithms publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2019.108286 – start-page: 882 year: 2011 ident: 10.1016/j.acha.2022.05.001_br0340 article-title: Greedy algorithms for structurally constrained high dimensional problems publication-title: Adv. Neural Inf. Process. Syst. – volume: 1 start-page: 586 issue: 4 year: 2007 ident: 10.1016/j.acha.2022.05.001_br0170 article-title: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems publication-title: IEEE J. Sel. Top. Signal Process. doi: 10.1109/JSTSP.2007.910281 – year: 2004 ident: 10.1016/j.acha.2022.05.001_br0060 – volume: 43 start-page: 1457 issue: 3 year: 2011 ident: 10.1016/j.acha.2022.05.001_br0020 article-title: Convergence rates for greedy algorithms in reduced basis methods publication-title: SIAM J. Math. Anal. doi: 10.1137/100795772 |
| SSID | ssj0011459 |
| Score | 2.411825 |
| Snippet | The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 489 |
| SubjectTerms | Banach space Biorthogonal Greedy Algorithm Convex optimization Greedy algorithm Sparsity |
| Title | Biorthogonal Greedy Algorithms in convex optimization |
| URI | https://dx.doi.org/10.1016/j.acha.2022.05.001 |
| Volume | 60 |
| WOSCitedRecordID | wos000808576100001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1096-603X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011459 issn: 1063-5203 databaseCode: AIEXJ dateStart: 20211207 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1RT9swELYmygN7QGOAYIwpD3urUrmJ4ySPZWJiiFVIQNW3yHUcKGuTqg2o_ffc2U4IDCGYtJeodevUujtdv7vcfUfIdx4wGUUpdbuCC5eJyAc_SEEhGYBTKuOY6Zzu4Czs96PhMD63U1EXepxAmOfRchnP_quqYQ2Uja2z71B3fVNYgNegdLiC2uH6JsUfjfFRTHGtU3xYVpOu2r3JdTEflzdTXf2qK82X7QK8xdS2YTYxagVMbcfb7K6sEoZIc60n5ghLZVLDYGWYoBbFvXY2nUGnTgmo6WQl_pgPBp1-p5lngBC1KqSyya-qAeZJfSYElD7EstT4KGXXYu5yqsf81k7WDA2wXpKZqUH2Dzcw3vYvX27SCrdgVzdIEOV5mmLVHukpR_YFngOP4WHnEcOWu5YXBjG4uVbv1_HwtH6w1GV6fl59bttHZUr-nv_Sy1ilgT8uP5FNGzg4PaPwLfJB5Z_JxwadJLz7XXPwLrZJ0DQExxiC82gIzjh3jCE4TUPYIVc_jy9_nLh2SIYrfUpLVyk_BdQmJFZchiAAFsrUZ1J1RzFNaSyk4twb8Qi52PwMELXMqOAySxm2iI78XbKWF7naIw5sYZ7AXmcpmZCwhWehDCFCzUYhOPZ90q3EkUjLII-DTCZJVSp4m6AIExRhQgOsl9wn7XrPzPCnvPrtoJJyYhGgQXYJGMUr-778474DsvFo6l_JWjm_U4dkXd6X48X8m7WdB9HrfkU |
| linkProvider | Elsevier |
| 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=Biorthogonal+Greedy+Algorithms+in+convex+optimization&rft.jtitle=Applied+and+computational+harmonic+analysis&rft.au=Dereventsov%2C+A.V.&rft.au=Temlyakov%2C+V.N.&rft.date=2022-09-01&rft.pub=Elsevier+Inc&rft.issn=1063-5203&rft.eissn=1096-603X&rft.volume=60&rft.spage=489&rft.epage=511&rft_id=info:doi/10.1016%2Fj.acha.2022.05.001&rft.externalDocID=S1063520322000410 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1063-5203&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1063-5203&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1063-5203&client=summon |