Generalized Univex Functions in Nonsmooth Multiobjective Optimization

Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes c...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kharbanda, Pallavi [verfasserIn] Agarwal, Divya [verfasserIn] Sinha, Deepa [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	Univex functions Type I functions Directional derivative Efficient solution

Übergeordnetes Werk:	Enthalten in: Journal of mathematical modelling and algorithms in operations research - Dordrecht : Springer Science + Business Media B.V., 2002, 12(2013), 4 vom: 09. März, Seite 393-406
Übergeordnetes Werk:	volume:12 ; year:2013 ; number:4 ; day:09 ; month:03 ; pages:393-406

Links:	Volltext

DOI / URN:	10.1007/s10852-013-9218-8

Katalog-ID:	SPR013747630

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allfields	10.1007/s10852-013-9218-8 doi (DE-627)SPR013747630 (SPR)s10852-013-9218-8-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 54.10 bkl 31.12 bkl 31.80 bkl 30.03 bkl Kharbanda, Pallavi verfasserin aut Generalized Univex Functions in Nonsmooth Multiobjective Optimization 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem. Univex functions (dpeaa)DE-He213 Type I functions (dpeaa)DE-He213 Directional derivative (dpeaa)DE-He213 Efficient solution (dpeaa)DE-He213 Agarwal, Divya verfasserin aut Sinha, Deepa verfasserin aut Enthalten in Journal of mathematical modelling and algorithms in operations research Dordrecht : Springer Science + Business Media B.V., 2002 12(2013), 4 vom: 09. März, Seite 393-406 (DE-627)352260467 (DE-600)2085150-9 1572-9214 nnns volume:12 year:2013 number:4 day:09 month:03 pages:393-406 https://dx.doi.org/10.1007/s10852-013-9218-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 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_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 54.10 ASE 31.12 ASE 31.80 ASE 30.03 ASE AR 12 2013 4 09 03 393-406
spelling	10.1007/s10852-013-9218-8 doi (DE-627)SPR013747630 (SPR)s10852-013-9218-8-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 54.10 bkl 31.12 bkl 31.80 bkl 30.03 bkl Kharbanda, Pallavi verfasserin aut Generalized Univex Functions in Nonsmooth Multiobjective Optimization 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem. Univex functions (dpeaa)DE-He213 Type I functions (dpeaa)DE-He213 Directional derivative (dpeaa)DE-He213 Efficient solution (dpeaa)DE-He213 Agarwal, Divya verfasserin aut Sinha, Deepa verfasserin aut Enthalten in Journal of mathematical modelling and algorithms in operations research Dordrecht : Springer Science + Business Media B.V., 2002 12(2013), 4 vom: 09. März, Seite 393-406 (DE-627)352260467 (DE-600)2085150-9 1572-9214 nnns volume:12 year:2013 number:4 day:09 month:03 pages:393-406 https://dx.doi.org/10.1007/s10852-013-9218-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 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_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 54.10 ASE 31.12 ASE 31.80 ASE 30.03 ASE AR 12 2013 4 09 03 393-406
allfields_unstemmed	10.1007/s10852-013-9218-8 doi (DE-627)SPR013747630 (SPR)s10852-013-9218-8-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 54.10 bkl 31.12 bkl 31.80 bkl 30.03 bkl Kharbanda, Pallavi verfasserin aut Generalized Univex Functions in Nonsmooth Multiobjective Optimization 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem. Univex functions (dpeaa)DE-He213 Type I functions (dpeaa)DE-He213 Directional derivative (dpeaa)DE-He213 Efficient solution (dpeaa)DE-He213 Agarwal, Divya verfasserin aut Sinha, Deepa verfasserin aut Enthalten in Journal of mathematical modelling and algorithms in operations research Dordrecht : Springer Science + Business Media B.V., 2002 12(2013), 4 vom: 09. März, Seite 393-406 (DE-627)352260467 (DE-600)2085150-9 1572-9214 nnns volume:12 year:2013 number:4 day:09 month:03 pages:393-406 https://dx.doi.org/10.1007/s10852-013-9218-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 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_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 54.10 ASE 31.12 ASE 31.80 ASE 30.03 ASE AR 12 2013 4 09 03 393-406
allfieldsGer	10.1007/s10852-013-9218-8 doi (DE-627)SPR013747630 (SPR)s10852-013-9218-8-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 54.10 bkl 31.12 bkl 31.80 bkl 30.03 bkl Kharbanda, Pallavi verfasserin aut Generalized Univex Functions in Nonsmooth Multiobjective Optimization 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem. Univex functions (dpeaa)DE-He213 Type I functions (dpeaa)DE-He213 Directional derivative (dpeaa)DE-He213 Efficient solution (dpeaa)DE-He213 Agarwal, Divya verfasserin aut Sinha, Deepa verfasserin aut Enthalten in Journal of mathematical modelling and algorithms in operations research Dordrecht : Springer Science + Business Media B.V., 2002 12(2013), 4 vom: 09. März, Seite 393-406 (DE-627)352260467 (DE-600)2085150-9 1572-9214 nnns volume:12 year:2013 number:4 day:09 month:03 pages:393-406 https://dx.doi.org/10.1007/s10852-013-9218-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 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_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 54.10 ASE 31.12 ASE 31.80 ASE 30.03 ASE AR 12 2013 4 09 03 393-406
allfieldsSound	10.1007/s10852-013-9218-8 doi (DE-627)SPR013747630 (SPR)s10852-013-9218-8-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 54.10 bkl 31.12 bkl 31.80 bkl 30.03 bkl Kharbanda, Pallavi verfasserin aut Generalized Univex Functions in Nonsmooth Multiobjective Optimization 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem. Univex functions (dpeaa)DE-He213 Type I functions (dpeaa)DE-He213 Directional derivative (dpeaa)DE-He213 Efficient solution (dpeaa)DE-He213 Agarwal, Divya verfasserin aut Sinha, Deepa verfasserin aut Enthalten in Journal of mathematical modelling and algorithms in operations research Dordrecht : Springer Science + Business Media B.V., 2002 12(2013), 4 vom: 09. März, Seite 393-406 (DE-627)352260467 (DE-600)2085150-9 1572-9214 nnns volume:12 year:2013 number:4 day:09 month:03 pages:393-406 https://dx.doi.org/10.1007/s10852-013-9218-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 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_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 54.10 ASE 31.12 ASE 31.80 ASE 30.03 ASE AR 12 2013 4 09 03 393-406
language	English
source	Enthalten in Journal of mathematical modelling and algorithms in operations research 12(2013), 4 vom: 09. März, Seite 393-406 volume:12 year:2013 number:4 day:09 month:03 pages:393-406
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author	Kharbanda, Pallavi
spellingShingle	Kharbanda, Pallavi ddc 510 bkl 54.10 bkl 31.12 bkl 31.80 bkl 30.03 misc Univex functions misc Type I functions misc Directional derivative misc Efficient solution Generalized Univex Functions in Nonsmooth Multiobjective Optimization
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topic_title	510 ASE 54.10 bkl 31.12 bkl 31.80 bkl 30.03 bkl Generalized Univex Functions in Nonsmooth Multiobjective Optimization Univex functions (dpeaa)DE-He213 Type I functions (dpeaa)DE-He213 Directional derivative (dpeaa)DE-He213 Efficient solution (dpeaa)DE-He213
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title_full	Generalized Univex Functions in Nonsmooth Multiobjective Optimization
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title_sort	generalized univex functions in nonsmooth multiobjective optimization
title_auth	Generalized Univex Functions in Nonsmooth Multiobjective Optimization
abstract	Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem.
abstractGer	Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem.
abstract_unstemmed	Abstract In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d − ρ − η − θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem.
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container_issue	4
title_short	Generalized Univex Functions in Nonsmooth Multiobjective Optimization
url	https://dx.doi.org/10.1007/s10852-013-9218-8
remote_bool	true
author2	Agarwal, Divya Sinha, Deepa
author2Str	Agarwal, Divya Sinha, Deepa
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doi_str	10.1007/s10852-013-9218-8
up_date	2024-07-03T21:53:47.798Z
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