On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings
Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex comb...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bauschke, Heinz H. [verfasserIn] Moursi, Walaa M. [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Foundations of Computational Mathematics - Springer-Verlag, 2001, 20(2020), 6 vom: 19. Feb., Seite 1653-1666 |
|---|---|
| Übergeordnetes Werk: |
volume:20 ; year:2020 ; number:6 ; day:19 ; month:02 ; pages:1653-1666 |
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| DOI / URN: |
10.1007/s10208-020-09449-w |
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| 520 | |a Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. | ||
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10.1007/s10208-020-09449-w doi (DE-627)SPR04205818X (SPR)s10208-020-09449-w-e DE-627 ger DE-627 rakwb eng Bauschke, Heinz H. verfasserin aut On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. Averaged nonexpansive mapping (dpeaa)DE-He213 Brezis–Haraux theorem (dpeaa)DE-He213 Displacement map (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Minimal displacement vector (dpeaa)DE-He213 Nonexpansive mapping (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 20(2020), 6 vom: 19. Feb., Seite 1653-1666 (DE-627)SPR009133062 nnns volume:20 year:2020 number:6 day:19 month:02 pages:1653-1666 https://dx.doi.org/10.1007/s10208-020-09449-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2020 6 19 02 1653-1666 |
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10.1007/s10208-020-09449-w doi (DE-627)SPR04205818X (SPR)s10208-020-09449-w-e DE-627 ger DE-627 rakwb eng Bauschke, Heinz H. verfasserin aut On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. Averaged nonexpansive mapping (dpeaa)DE-He213 Brezis–Haraux theorem (dpeaa)DE-He213 Displacement map (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Minimal displacement vector (dpeaa)DE-He213 Nonexpansive mapping (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 20(2020), 6 vom: 19. Feb., Seite 1653-1666 (DE-627)SPR009133062 nnns volume:20 year:2020 number:6 day:19 month:02 pages:1653-1666 https://dx.doi.org/10.1007/s10208-020-09449-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2020 6 19 02 1653-1666 |
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10.1007/s10208-020-09449-w doi (DE-627)SPR04205818X (SPR)s10208-020-09449-w-e DE-627 ger DE-627 rakwb eng Bauschke, Heinz H. verfasserin aut On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. Averaged nonexpansive mapping (dpeaa)DE-He213 Brezis–Haraux theorem (dpeaa)DE-He213 Displacement map (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Minimal displacement vector (dpeaa)DE-He213 Nonexpansive mapping (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 20(2020), 6 vom: 19. Feb., Seite 1653-1666 (DE-627)SPR009133062 nnns volume:20 year:2020 number:6 day:19 month:02 pages:1653-1666 https://dx.doi.org/10.1007/s10208-020-09449-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2020 6 19 02 1653-1666 |
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10.1007/s10208-020-09449-w doi (DE-627)SPR04205818X (SPR)s10208-020-09449-w-e DE-627 ger DE-627 rakwb eng Bauschke, Heinz H. verfasserin aut On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. Averaged nonexpansive mapping (dpeaa)DE-He213 Brezis–Haraux theorem (dpeaa)DE-He213 Displacement map (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Minimal displacement vector (dpeaa)DE-He213 Nonexpansive mapping (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 20(2020), 6 vom: 19. Feb., Seite 1653-1666 (DE-627)SPR009133062 nnns volume:20 year:2020 number:6 day:19 month:02 pages:1653-1666 https://dx.doi.org/10.1007/s10208-020-09449-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2020 6 19 02 1653-1666 |
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10.1007/s10208-020-09449-w doi (DE-627)SPR04205818X (SPR)s10208-020-09449-w-e DE-627 ger DE-627 rakwb eng Bauschke, Heinz H. verfasserin aut On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. Averaged nonexpansive mapping (dpeaa)DE-He213 Brezis–Haraux theorem (dpeaa)DE-He213 Displacement map (dpeaa)DE-He213 Maximally monotone operator (dpeaa)DE-He213 Minimal displacement vector (dpeaa)DE-He213 Nonexpansive mapping (dpeaa)DE-He213 Resolvent (dpeaa)DE-He213 Moursi, Walaa M. verfasserin aut Enthalten in Foundations of Computational Mathematics Springer-Verlag, 2001 20(2020), 6 vom: 19. Feb., Seite 1653-1666 (DE-627)SPR009133062 nnns volume:20 year:2020 number:6 day:19 month:02 pages:1653-1666 https://dx.doi.org/10.1007/s10208-020-09449-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2020 6 19 02 1653-1666 |
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Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. |
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Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. |
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Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. Various examples illustrate the tightness of our results. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR04205818X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201126070740.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201126s2020 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10208-020-09449-w</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR04205818X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10208-020-09449-w-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">Bauschke, Heinz H.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the Minimal Displacement Vector of Compositions and Convex Combinations of Nonexpansive Mappings</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</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="520" ind1=" " ind2=" "><subfield code="a">Abstract Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. It was shown in 2012 that if finitely many firmly nonexpansive mappings have or “almost have” fixed points, then the same is true for compositions and convex combinations. More recently, sharp information about the minimal displacement vector of compositions and of convex combinations of firmly nonexpansive mappings was obtained in terms of the displacement vectors of the underlying operators. Using a new proof technique based on the Brezis–Haraux theorem and reflected resolvents, we extend these results from firmly nonexpansive to general averaged nonexpansive mappings. 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Feb., Seite 1653-1666</subfield><subfield code="w">(DE-627)SPR009133062</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:20</subfield><subfield code="g">year:2020</subfield><subfield code="g">number:6</subfield><subfield code="g">day:19</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:1653-1666</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s10208-020-09449-w</subfield><subfield code="z">lizenzpflichtig</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">20</subfield><subfield code="j">2020</subfield><subfield code="e">6</subfield><subfield code="b">19</subfield><subfield code="c">02</subfield><subfield code="h">1653-1666</subfield></datafield></record></collection>
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