Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence
Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and ho...
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| Autor*in: |
Hernández, Elvira [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Applied mathematics & optimization - Springer US, 1974, 86(2022), 1 vom: 07. Juni |
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| Übergeordnetes Werk: |
volume:86 ; year:2022 ; number:1 ; day:07 ; month:06 |
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| DOI / URN: |
10.1007/s00245-022-09879-8 |
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OLC2078850985 |
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| 520 | |a Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. | ||
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10.1007/s00245-022-09879-8 doi (DE-627)OLC2078850985 (DE-He213)s00245-022-09879-8-p DE-627 ger DE-627 rakwb eng 510 VZ Hernández, Elvira verfasserin aut Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. Set-valued map Set-valued optimization problem Asymptotic map Epi-convergence Total epi-convergence Stability López, Rubén (orcid)0000-0002-2975-7109 aut Enthalten in Applied mathematics & optimization Springer US, 1974 86(2022), 1 vom: 07. Juni (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:86 year:2022 number:1 day:07 month:06 https://doi.org/10.1007/s00245-022-09879-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4027 AR 86 2022 1 07 06 |
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10.1007/s00245-022-09879-8 doi (DE-627)OLC2078850985 (DE-He213)s00245-022-09879-8-p DE-627 ger DE-627 rakwb eng 510 VZ Hernández, Elvira verfasserin aut Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. Set-valued map Set-valued optimization problem Asymptotic map Epi-convergence Total epi-convergence Stability López, Rubén (orcid)0000-0002-2975-7109 aut Enthalten in Applied mathematics & optimization Springer US, 1974 86(2022), 1 vom: 07. Juni (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:86 year:2022 number:1 day:07 month:06 https://doi.org/10.1007/s00245-022-09879-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4027 AR 86 2022 1 07 06 |
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10.1007/s00245-022-09879-8 doi (DE-627)OLC2078850985 (DE-He213)s00245-022-09879-8-p DE-627 ger DE-627 rakwb eng 510 VZ Hernández, Elvira verfasserin aut Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. Set-valued map Set-valued optimization problem Asymptotic map Epi-convergence Total epi-convergence Stability López, Rubén (orcid)0000-0002-2975-7109 aut Enthalten in Applied mathematics & optimization Springer US, 1974 86(2022), 1 vom: 07. Juni (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:86 year:2022 number:1 day:07 month:06 https://doi.org/10.1007/s00245-022-09879-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4027 AR 86 2022 1 07 06 |
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10.1007/s00245-022-09879-8 doi (DE-627)OLC2078850985 (DE-He213)s00245-022-09879-8-p DE-627 ger DE-627 rakwb eng 510 VZ Hernández, Elvira verfasserin aut Stability in Set-Valued Optimization Problems Using Asymptotic Analysis and Epi-Convergence 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. Set-valued map Set-valued optimization problem Asymptotic map Epi-convergence Total epi-convergence Stability López, Rubén (orcid)0000-0002-2975-7109 aut Enthalten in Applied mathematics & optimization Springer US, 1974 86(2022), 1 vom: 07. Juni (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:86 year:2022 number:1 day:07 month:06 https://doi.org/10.1007/s00245-022-09879-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4027 AR 86 2022 1 07 06 |
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Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract We study the stability of set-valued optimization problems by using epi-convergence coupled with asymptotic analysis. To do this, we recall the notion of epi-convergence and introduce the notion of total epi-convergence for set-valued maps. We characterize them by means of epi-limits and horizon epi-limits. We use these epi-limits to study the behavior of vector/set type solutions and level/colevel sets under variations of the whole data. We also introduce several stronger epi-convergence notions and use them to study the stability of solution sets and minimal solution sets. We extend and generalize various results from the literature since we deal with unbounded feasible sets and objective maps. Finally, to illustrate our main results, we apply them to various classes of set-valued maps. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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López, Rubén |
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10.1007/s00245-022-09879-8 |
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2024-07-03T22:25:06.726Z |
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