New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization

Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and p...
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Autor*in:	Gutiérrez, C. [verfasserIn] Jiménez, B. Novo, V.

Format:	Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set

Systematik:	SA 6420 SA 6420

Anmerkung:	© Springer Science+Business Media, LLC 2009

Übergeordnetes Werk:	Enthalten in: Journal of optimization theory and applications - Springer US, 1967, 142(2009), 1 vom: 27. Feb., Seite 85-106
Übergeordnetes Werk:	volume:142 ; year:2009 ; number:1 ; day:27 ; month:02 ; pages:85-106

Links:	Volltext

DOI / URN:	10.1007/s10957-009-9525-4

Katalog-ID:	OLC202648838X

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allfields	10.1007/s10957-009-9525-4 doi (DE-627)OLC202648838X (DE-He213)s10957-009-9525-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Gutiérrez, C. verfasserin aut New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2009 Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set Jiménez, B. aut Novo, V. aut Enthalten in Journal of optimization theory and applications Springer US, 1967 142(2009), 1 vom: 27. Feb., Seite 85-106 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:142 year:2009 number:1 day:27 month:02 pages:85-106 https://doi.org/10.1007/s10957-009-9525-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 142 2009 1 27 02 85-106
spelling	10.1007/s10957-009-9525-4 doi (DE-627)OLC202648838X (DE-He213)s10957-009-9525-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Gutiérrez, C. verfasserin aut New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2009 Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set Jiménez, B. aut Novo, V. aut Enthalten in Journal of optimization theory and applications Springer US, 1967 142(2009), 1 vom: 27. Feb., Seite 85-106 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:142 year:2009 number:1 day:27 month:02 pages:85-106 https://doi.org/10.1007/s10957-009-9525-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 142 2009 1 27 02 85-106
allfields_unstemmed	10.1007/s10957-009-9525-4 doi (DE-627)OLC202648838X (DE-He213)s10957-009-9525-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Gutiérrez, C. verfasserin aut New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2009 Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set Jiménez, B. aut Novo, V. aut Enthalten in Journal of optimization theory and applications Springer US, 1967 142(2009), 1 vom: 27. Feb., Seite 85-106 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:142 year:2009 number:1 day:27 month:02 pages:85-106 https://doi.org/10.1007/s10957-009-9525-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 142 2009 1 27 02 85-106
allfieldsGer	10.1007/s10957-009-9525-4 doi (DE-627)OLC202648838X (DE-He213)s10957-009-9525-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Gutiérrez, C. verfasserin aut New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2009 Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set Jiménez, B. aut Novo, V. aut Enthalten in Journal of optimization theory and applications Springer US, 1967 142(2009), 1 vom: 27. Feb., Seite 85-106 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:142 year:2009 number:1 day:27 month:02 pages:85-106 https://doi.org/10.1007/s10957-009-9525-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 142 2009 1 27 02 85-106
allfieldsSound	10.1007/s10957-009-9525-4 doi (DE-627)OLC202648838X (DE-He213)s10957-009-9525-4-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Gutiérrez, C. verfasserin aut New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2009 Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set Jiménez, B. aut Novo, V. aut Enthalten in Journal of optimization theory and applications Springer US, 1967 142(2009), 1 vom: 27. Feb., Seite 85-106 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:142 year:2009 number:1 day:27 month:02 pages:85-106 https://doi.org/10.1007/s10957-009-9525-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 142 2009 1 27 02 85-106
language	English
source	Enthalten in Journal of optimization theory and applications 142(2009), 1 vom: 27. Feb., Seite 85-106 volume:142 year:2009 number:1 day:27 month:02 pages:85-106
sourceStr	Enthalten in Journal of optimization theory and applications 142(2009), 1 vom: 27. Feb., Seite 85-106 volume:142 year:2009 number:1 day:27 month:02 pages:85-106
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Second order directional derivative Optimality conditions Vector optimization Scalarization Second order tangent set
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container_title	Journal of optimization theory and applications
authorswithroles_txt_mv	Gutiérrez, C. @@aut@@ Jiménez, B. @@aut@@ Novo, V. @@aut@@
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author	Gutiérrez, C.
spellingShingle	Gutiérrez, C. ddc 330 ssgn 17,1 rvk SA 6420 misc Second order directional derivative misc Optimality conditions misc Vector optimization misc Scalarization misc Second order tangent set New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
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title	New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
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title_full	New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
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title_sort	new second-order directional derivative and optimality conditions in scalar and vector optimization
title_auth	New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
abstract	Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. © Springer Science+Business Media, LLC 2009
abstractGer	Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. © Springer Science+Business Media, LLC 2009
abstract_unstemmed	Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. © Springer Science+Business Media, LLC 2009
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title_short	New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
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up_date	2024-07-04T04:04:57.690Z
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