On compositions of special cases of Lipschitz continuous operators
Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of suc...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Giselsson, Pontus [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2021 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© The Author(s) 2021 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Fixed point theory and applications - Heidelberg : Springer, 2004, 2021(2021), 1 vom: 20. Dez. |
|---|---|
| Übergeordnetes Werk: |
volume:2021 ; year:2021 ; number:1 ; day:20 ; month:12 |
| Links: |
|---|
| DOI / URN: |
10.1186/s13663-021-00709-0 |
|---|
| Katalog-ID: |
SPR045820902 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | SPR045820902 | ||
| 003 | DE-627 | ||
| 005 | 20230509100141.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 211220s2021 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1186/s13663-021-00709-0 |2 doi | |
| 035 | |a (DE-627)SPR045820902 | ||
| 035 | |a (SPR)s13663-021-00709-0-e | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Giselsson, Pontus |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On compositions of special cases of Lipschitz continuous operators |
| 264 | 1 | |c 2021 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a © The Author(s) 2021 | ||
| 520 | |a Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. | ||
| 650 | 4 | |a Compositions of operators |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Conically nonexpansive operators |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Douglas–Rachford algorithm |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Forward-backward algorithm |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hypoconvex function |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Maximally monotone operator |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Proximal operator |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Resolvent |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Moursi, Walaa M. |0 (orcid)0000-0002-0113-9309 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Fixed point theory and applications |d Heidelberg : Springer, 2004 |g 2021(2021), 1 vom: 20. Dez. |w (DE-627)379482037 |w (DE-600)2135860-6 |x 1687-1812 |7 nnns |
| 773 | 1 | 8 | |g volume:2021 |g year:2021 |g number:1 |g day:20 |g month:12 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1186/s13663-021-00709-0 |z kostenfrei |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_SPRINGER | ||
| 951 | |a AR | ||
| 952 | |d 2021 |j 2021 |e 1 |b 20 |c 12 | ||
| author_variant |
p g pg w m m wm wmm |
|---|---|
| matchkey_str |
article:16871812:2021----::nopstosfpcacssfishtcn |
| hierarchy_sort_str |
2021 |
| publishDate |
2021 |
| allfields |
10.1186/s13663-021-00709-0 doi (DE-627)SPR045820902 (SPR)s13663-021-00709-0-e DE-627 ger DE-627 rakwb eng Giselsson, Pontus verfasserin aut On compositions of special cases of Lipschitz continuous operators 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. Compositions of operators (dpeaa)DE-He213 Conically nonexpansive operators (dpeaa)DE-He213 Douglas–Rachford algorithm (dpeaa)DE-He213 Forward-backward algorithm (dpeaa)DE-He213 Hypoconvex function (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. (orcid)0000-0002-0113-9309 aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2021(2021), 1 vom: 20. Dez. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2021 year:2021 number:1 day:20 month:12 https://dx.doi.org/10.1186/s13663-021-00709-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2021 2021 1 20 12 |
| spelling |
10.1186/s13663-021-00709-0 doi (DE-627)SPR045820902 (SPR)s13663-021-00709-0-e DE-627 ger DE-627 rakwb eng Giselsson, Pontus verfasserin aut On compositions of special cases of Lipschitz continuous operators 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. Compositions of operators (dpeaa)DE-He213 Conically nonexpansive operators (dpeaa)DE-He213 Douglas–Rachford algorithm (dpeaa)DE-He213 Forward-backward algorithm (dpeaa)DE-He213 Hypoconvex function (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. (orcid)0000-0002-0113-9309 aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2021(2021), 1 vom: 20. Dez. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2021 year:2021 number:1 day:20 month:12 https://dx.doi.org/10.1186/s13663-021-00709-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2021 2021 1 20 12 |
| allfields_unstemmed |
10.1186/s13663-021-00709-0 doi (DE-627)SPR045820902 (SPR)s13663-021-00709-0-e DE-627 ger DE-627 rakwb eng Giselsson, Pontus verfasserin aut On compositions of special cases of Lipschitz continuous operators 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. Compositions of operators (dpeaa)DE-He213 Conically nonexpansive operators (dpeaa)DE-He213 Douglas–Rachford algorithm (dpeaa)DE-He213 Forward-backward algorithm (dpeaa)DE-He213 Hypoconvex function (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. (orcid)0000-0002-0113-9309 aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2021(2021), 1 vom: 20. Dez. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2021 year:2021 number:1 day:20 month:12 https://dx.doi.org/10.1186/s13663-021-00709-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2021 2021 1 20 12 |
| allfieldsGer |
10.1186/s13663-021-00709-0 doi (DE-627)SPR045820902 (SPR)s13663-021-00709-0-e DE-627 ger DE-627 rakwb eng Giselsson, Pontus verfasserin aut On compositions of special cases of Lipschitz continuous operators 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. Compositions of operators (dpeaa)DE-He213 Conically nonexpansive operators (dpeaa)DE-He213 Douglas–Rachford algorithm (dpeaa)DE-He213 Forward-backward algorithm (dpeaa)DE-He213 Hypoconvex function (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. (orcid)0000-0002-0113-9309 aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2021(2021), 1 vom: 20. Dez. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2021 year:2021 number:1 day:20 month:12 https://dx.doi.org/10.1186/s13663-021-00709-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2021 2021 1 20 12 |
| allfieldsSound |
10.1186/s13663-021-00709-0 doi (DE-627)SPR045820902 (SPR)s13663-021-00709-0-e DE-627 ger DE-627 rakwb eng Giselsson, Pontus verfasserin aut On compositions of special cases of Lipschitz continuous operators 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. Compositions of operators (dpeaa)DE-He213 Conically nonexpansive operators (dpeaa)DE-He213 Douglas–Rachford algorithm (dpeaa)DE-He213 Forward-backward algorithm (dpeaa)DE-He213 Hypoconvex function (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. (orcid)0000-0002-0113-9309 aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2021(2021), 1 vom: 20. Dez. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2021 year:2021 number:1 day:20 month:12 https://dx.doi.org/10.1186/s13663-021-00709-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2021 2021 1 20 12 |
| language |
English |
| source |
Enthalten in Fixed point theory and applications 2021(2021), 1 vom: 20. Dez. volume:2021 year:2021 number:1 day:20 month:12 |
| sourceStr |
Enthalten in Fixed point theory and applications 2021(2021), 1 vom: 20. Dez. volume:2021 year:2021 number:1 day:20 month:12 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Compositions of operators Conically nonexpansive operators Douglas–Rachford algorithm Forward-backward algorithm Hypoconvex function Maximally monotone operator Proximal operator Resolvent |
| isfreeaccess_bool |
true |
| container_title |
Fixed point theory and applications |
| authorswithroles_txt_mv |
Giselsson, Pontus @@aut@@ Moursi, Walaa M. @@aut@@ |
| publishDateDaySort_date |
2021-12-20T00:00:00Z |
| hierarchy_top_id |
379482037 |
| id |
SPR045820902 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR045820902</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509100141.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">211220s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1186/s13663-021-00709-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR045820902</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13663-021-00709-0-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Giselsson, Pontus</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On compositions of special cases of Lipschitz continuous operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Compositions of operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Conically nonexpansive operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Douglas–Rachford algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Forward-backward algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hypoconvex function</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maximally monotone operator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proximal operator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Resolvent</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Moursi, Walaa M.</subfield><subfield code="0">(orcid)0000-0002-0113-9309</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Fixed point theory and applications</subfield><subfield code="d">Heidelberg : Springer, 2004</subfield><subfield code="g">2021(2021), 1 vom: 20. Dez.</subfield><subfield code="w">(DE-627)379482037</subfield><subfield code="w">(DE-600)2135860-6</subfield><subfield code="x">1687-1812</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:2021</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:1</subfield><subfield code="g">day:20</subfield><subfield code="g">month:12</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1186/s13663-021-00709-0</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">2021</subfield><subfield code="j">2021</subfield><subfield code="e">1</subfield><subfield code="b">20</subfield><subfield code="c">12</subfield></datafield></record></collection>
|
| author |
Giselsson, Pontus |
| spellingShingle |
Giselsson, Pontus misc Compositions of operators misc Conically nonexpansive operators misc Douglas–Rachford algorithm misc Forward-backward algorithm misc Hypoconvex function misc Maximally monotone operator misc Proximal operator misc Resolvent On compositions of special cases of Lipschitz continuous operators |
| authorStr |
Giselsson, Pontus |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)379482037 |
| format |
electronic Article |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
springer |
| remote_str |
true |
| illustrated |
Not Illustrated |
| issn |
1687-1812 |
| topic_title |
On compositions of special cases of Lipschitz continuous operators Compositions of operators (dpeaa)DE-He213 Conically nonexpansive operators (dpeaa)DE-He213 Douglas–Rachford algorithm (dpeaa)DE-He213 Forward-backward algorithm (dpeaa)DE-He213 Hypoconvex function (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 |
| topic |
misc Compositions of operators misc Conically nonexpansive operators misc Douglas–Rachford algorithm misc Forward-backward algorithm misc Hypoconvex function misc Maximally monotone operator misc Proximal operator misc Resolvent |
| topic_unstemmed |
misc Compositions of operators misc Conically nonexpansive operators misc Douglas–Rachford algorithm misc Forward-backward algorithm misc Hypoconvex function misc Maximally monotone operator misc Proximal operator misc Resolvent |
| topic_browse |
misc Compositions of operators misc Conically nonexpansive operators misc Douglas–Rachford algorithm misc Forward-backward algorithm misc Hypoconvex function misc Maximally monotone operator misc Proximal operator misc Resolvent |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
Fixed point theory and applications |
| hierarchy_parent_id |
379482037 |
| hierarchy_top_title |
Fixed point theory and applications |
| isfreeaccess_txt |
true |
| familylinks_str_mv |
(DE-627)379482037 (DE-600)2135860-6 |
| title |
On compositions of special cases of Lipschitz continuous operators |
| ctrlnum |
(DE-627)SPR045820902 (SPR)s13663-021-00709-0-e |
| title_full |
On compositions of special cases of Lipschitz continuous operators |
| author_sort |
Giselsson, Pontus |
| journal |
Fixed point theory and applications |
| journalStr |
Fixed point theory and applications |
| lang_code |
eng |
| isOA_bool |
true |
| recordtype |
marc |
| publishDateSort |
2021 |
| contenttype_str_mv |
txt |
| author_browse |
Giselsson, Pontus Moursi, Walaa M. |
| container_volume |
2021 |
| format_se |
Elektronische Aufsätze |
| author-letter |
Giselsson, Pontus |
| doi_str_mv |
10.1186/s13663-021-00709-0 |
| normlink |
(ORCID)0000-0002-0113-9309 |
| normlink_prefix_str_mv |
(orcid)0000-0002-0113-9309 |
| title_sort |
on compositions of special cases of lipschitz continuous operators |
| title_auth |
On compositions of special cases of Lipschitz continuous operators |
| abstract |
Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. © The Author(s) 2021 |
| abstractGer |
Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. © The Author(s) 2021 |
| abstract_unstemmed |
Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions. © The Author(s) 2021 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER |
| container_issue |
1 |
| title_short |
On compositions of special cases of Lipschitz continuous operators |
| url |
https://dx.doi.org/10.1186/s13663-021-00709-0 |
| remote_bool |
true |
| author2 |
Moursi, Walaa M. |
| author2Str |
Moursi, Walaa M. |
| ppnlink |
379482037 |
| mediatype_str_mv |
c |
| isOA_txt |
true |
| hochschulschrift_bool |
false |
| doi_str |
10.1186/s13663-021-00709-0 |
| up_date |
2024-07-03T18:29:35.973Z |
| _version_ |
1803583620098555904 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR045820902</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509100141.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">211220s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1186/s13663-021-00709-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR045820902</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13663-021-00709-0-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Giselsson, Pontus</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On compositions of special cases of Lipschitz continuous operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Compositions of operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Conically nonexpansive operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Douglas–Rachford algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Forward-backward algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hypoconvex function</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maximally monotone operator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proximal operator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Resolvent</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Moursi, Walaa M.</subfield><subfield code="0">(orcid)0000-0002-0113-9309</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Fixed point theory and applications</subfield><subfield code="d">Heidelberg : Springer, 2004</subfield><subfield code="g">2021(2021), 1 vom: 20. Dez.</subfield><subfield code="w">(DE-627)379482037</subfield><subfield code="w">(DE-600)2135860-6</subfield><subfield code="x">1687-1812</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:2021</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:1</subfield><subfield code="g">day:20</subfield><subfield code="g">month:12</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1186/s13663-021-00709-0</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">2021</subfield><subfield code="j">2021</subfield><subfield code="e">1</subfield><subfield code="b">20</subfield><subfield code="c">12</subfield></datafield></record></collection>
|
| score |
7.400941 |