Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems
Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex con...
Ausführliche Beschreibung
Autor*in: |
Dinh, Nguyen [verfasserIn] Long, Dang Hai [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2018 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Vietnam journal of mathematics - Singapore : Springer, 1999, 46(2018), 2 vom: 17. März, Seite 293-328 |
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Übergeordnetes Werk: |
volume:46 ; year:2018 ; number:2 ; day:17 ; month:03 ; pages:293-328 |
Links: |
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DOI / URN: |
10.1007/s10013-018-0283-1 |
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Katalog-ID: |
SPR008017158 |
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520 | |a Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. | ||
650 | 4 | |a Robust vector optimization |7 (dpeaa)DE-He213 | |
650 | 4 | |a Robust convex optimization |7 (dpeaa)DE-He213 | |
650 | 4 | |a Vector optimization |7 (dpeaa)DE-He213 | |
650 | 4 | |a Robust strong duality |7 (dpeaa)DE-He213 | |
650 | 4 | |a Vector Farkas lemma |7 (dpeaa)DE-He213 | |
700 | 1 | |a Long, Dang Hai |e verfasserin |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Vietnam journal of mathematics |d Singapore : Springer, 1999 |g 46(2018), 2 vom: 17. März, Seite 293-328 |w (DE-627)300183968 |w (DE-600)1481450-X |x 2305-2228 |7 nnns |
773 | 1 | 8 | |g volume:46 |g year:2018 |g number:2 |g day:17 |g month:03 |g pages:293-328 |
856 | 4 | 0 | |u https://dx.doi.org/10.1007/s10013-018-0283-1 |z lizenzpflichtig |3 Volltext |
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10.1007/s10013-018-0283-1 doi (DE-627)SPR008017158 (SPR)s10013-018-0283-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Dinh, Nguyen verfasserin aut Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. Robust vector optimization (dpeaa)DE-He213 Robust convex optimization (dpeaa)DE-He213 Vector optimization (dpeaa)DE-He213 Robust strong duality (dpeaa)DE-He213 Vector Farkas lemma (dpeaa)DE-He213 Long, Dang Hai verfasserin aut Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 46(2018), 2 vom: 17. März, Seite 293-328 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:46 year:2018 number:2 day:17 month:03 pages:293-328 https://dx.doi.org/10.1007/s10013-018-0283-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 46 2018 2 17 03 293-328 |
spelling |
10.1007/s10013-018-0283-1 doi (DE-627)SPR008017158 (SPR)s10013-018-0283-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Dinh, Nguyen verfasserin aut Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. Robust vector optimization (dpeaa)DE-He213 Robust convex optimization (dpeaa)DE-He213 Vector optimization (dpeaa)DE-He213 Robust strong duality (dpeaa)DE-He213 Vector Farkas lemma (dpeaa)DE-He213 Long, Dang Hai verfasserin aut Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 46(2018), 2 vom: 17. März, Seite 293-328 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:46 year:2018 number:2 day:17 month:03 pages:293-328 https://dx.doi.org/10.1007/s10013-018-0283-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 46 2018 2 17 03 293-328 |
allfields_unstemmed |
10.1007/s10013-018-0283-1 doi (DE-627)SPR008017158 (SPR)s10013-018-0283-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Dinh, Nguyen verfasserin aut Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. Robust vector optimization (dpeaa)DE-He213 Robust convex optimization (dpeaa)DE-He213 Vector optimization (dpeaa)DE-He213 Robust strong duality (dpeaa)DE-He213 Vector Farkas lemma (dpeaa)DE-He213 Long, Dang Hai verfasserin aut Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 46(2018), 2 vom: 17. März, Seite 293-328 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:46 year:2018 number:2 day:17 month:03 pages:293-328 https://dx.doi.org/10.1007/s10013-018-0283-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 46 2018 2 17 03 293-328 |
allfieldsGer |
10.1007/s10013-018-0283-1 doi (DE-627)SPR008017158 (SPR)s10013-018-0283-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Dinh, Nguyen verfasserin aut Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. Robust vector optimization (dpeaa)DE-He213 Robust convex optimization (dpeaa)DE-He213 Vector optimization (dpeaa)DE-He213 Robust strong duality (dpeaa)DE-He213 Vector Farkas lemma (dpeaa)DE-He213 Long, Dang Hai verfasserin aut Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 46(2018), 2 vom: 17. März, Seite 293-328 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:46 year:2018 number:2 day:17 month:03 pages:293-328 https://dx.doi.org/10.1007/s10013-018-0283-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 46 2018 2 17 03 293-328 |
allfieldsSound |
10.1007/s10013-018-0283-1 doi (DE-627)SPR008017158 (SPR)s10013-018-0283-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Dinh, Nguyen verfasserin aut Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. Robust vector optimization (dpeaa)DE-He213 Robust convex optimization (dpeaa)DE-He213 Vector optimization (dpeaa)DE-He213 Robust strong duality (dpeaa)DE-He213 Vector Farkas lemma (dpeaa)DE-He213 Long, Dang Hai verfasserin aut Enthalten in Vietnam journal of mathematics Singapore : Springer, 1999 46(2018), 2 vom: 17. März, Seite 293-328 (DE-627)300183968 (DE-600)1481450-X 2305-2228 nnns volume:46 year:2018 number:2 day:17 month:03 pages:293-328 https://dx.doi.org/10.1007/s10013-018-0283-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 46 2018 2 17 03 293-328 |
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Enthalten in Vietnam journal of mathematics 46(2018), 2 vom: 17. März, Seite 293-328 volume:46 year:2018 number:2 day:17 month:03 pages:293-328 |
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Enthalten in Vietnam journal of mathematics 46(2018), 2 vom: 17. März, Seite 293-328 volume:46 year:2018 number:2 day:17 month:03 pages:293-328 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR008017158</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110200552.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10013-018-0283-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR008017158</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10013-018-0283-1-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="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dinh, Nguyen</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</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 Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. 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Dinh, Nguyen |
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Dinh, Nguyen ddc 510 bkl 31.00 misc Robust vector optimization misc Robust convex optimization misc Vector optimization misc Robust strong duality misc Vector Farkas lemma Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems |
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510 ASE 31.00 bkl Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems Robust vector optimization (dpeaa)DE-He213 Robust convex optimization (dpeaa)DE-He213 Vector optimization (dpeaa)DE-He213 Robust strong duality (dpeaa)DE-He213 Vector Farkas lemma (dpeaa)DE-He213 |
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ddc 510 bkl 31.00 misc Robust vector optimization misc Robust convex optimization misc Vector optimization misc Robust strong duality misc Vector Farkas lemma |
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complete characterizations of robust strong duality for robust vector optimization problems |
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Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems |
abstract |
Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. |
abstractGer |
Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. |
abstract_unstemmed |
Abstract Consider the robust vector optimization problem of the model(RVP)WMin{F(x):x∈C,Gu(x)∈−S∀u∈U},%$\text{(RVP)}\qquad \text{WMin}\{F(x):~ x\in C,~ G_{u}(x)\in -S~ \forall u\in \mathcal{U}\} , %$ where X, Y, and Z are locally convex Hausdorff topological vector spaces, S is a nonempty convex cone in Z, C ⊂ X is a nonempty subset, $\mathcal {U}$ is an uncertainty set, and F : X → Y ∪{ + ∞Y}, Gu : X → Z ∪{ + ∞Z} for all $u\in \mathcal {U}$. The Lagrangian robust dual problem and the weakly Lagrangian robust dual problem for (RVP) are proposed and then principles of robust strong duality for (RVP) associated to these two dual problems in a general setting (not necessarily convex) are established. The results are obtained based mainly on the robust vector Farkas-type results and the representations of epigraphs of conjugate mappings of vector-valued functions, which are the key tools of this paper. Next, we give characterizations of robust strong duality for (RVP) in the convex setting and also for vector optimization problems (i.e., when the uncertainty set is a singleton). To illustrate the ability of applications of the results just obtained, we show that when specifying our general results for (RVP) to robust scalar problems (i.e., when $Y = \mathbb {R}$), we get new principles of robust strong duality for general non-convex robust problems, and various characterizations of robust strong duality for convex problems which cover/extend known results in the literature. In addition, we consider a (scalar) robust infinite problem. It turns out that a further application of the general results obtained for scalar robust problems to this specific problem also leads to various forms of robust strong duality results for the problem in consideration, which are new or cover/extend the known ones published in the recent years. |
collection_details |
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container_issue |
2 |
title_short |
Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems |
url |
https://dx.doi.org/10.1007/s10013-018-0283-1 |
remote_bool |
true |
author2 |
Long, Dang Hai |
author2Str |
Long, Dang Hai |
ppnlink |
300183968 |
mediatype_str_mv |
c |
isOA_txt |
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hochschulschrift_bool |
false |
doi_str |
10.1007/s10013-018-0283-1 |
up_date |
2024-07-03T16:47:12.675Z |
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1803577178386857984 |
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score |
7.3976707 |