Interval-based KKT framework for support vector machines and beyond

Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Awais Younus [verfasserIn] Rimsha [verfasserIn] Cemil Tunç [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines

Übergeordnetes Werk:	In: Journal of Taibah University for Science - Taylor & Francis Group, 2016, 18(2024), 1
Übergeordnetes Werk:	volume:18 ; year:2024 ; number:1

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1080/16583655.2024.2334017

Katalog-ID:	DOAJ099798255

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spelling	10.1080/16583655.2024.2334017 doi (DE-627)DOAJ099798255 (DE-599)DOAJ13e4f07c3a614c65831a0f9ba2e8038f DE-627 ger DE-627 rakwb eng Q1-390 Awais Younus verfasserin aut Interval-based KKT framework for support vector machines and beyond 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results. Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines Science (General) Rimsha verfasserin aut Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 18(2024), 1 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:18 year:2024 number:1 https://doi.org/10.1080/16583655.2024.2334017 kostenfrei https://doaj.org/article/13e4f07c3a614c65831a0f9ba2e8038f kostenfrei https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2024 1
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allfieldsGer	10.1080/16583655.2024.2334017 doi (DE-627)DOAJ099798255 (DE-599)DOAJ13e4f07c3a614c65831a0f9ba2e8038f DE-627 ger DE-627 rakwb eng Q1-390 Awais Younus verfasserin aut Interval-based KKT framework for support vector machines and beyond 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results. Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines Science (General) Rimsha verfasserin aut Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 18(2024), 1 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:18 year:2024 number:1 https://doi.org/10.1080/16583655.2024.2334017 kostenfrei https://doaj.org/article/13e4f07c3a614c65831a0f9ba2e8038f kostenfrei https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2024 1
allfieldsSound	10.1080/16583655.2024.2334017 doi (DE-627)DOAJ099798255 (DE-599)DOAJ13e4f07c3a614c65831a0f9ba2e8038f DE-627 ger DE-627 rakwb eng Q1-390 Awais Younus verfasserin aut Interval-based KKT framework for support vector machines and beyond 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results. Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines Science (General) Rimsha verfasserin aut Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 18(2024), 1 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:18 year:2024 number:1 https://doi.org/10.1080/16583655.2024.2334017 kostenfrei https://doaj.org/article/13e4f07c3a614c65831a0f9ba2e8038f kostenfrei https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 18 2024 1
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callnumber-first	Q - Science
author	Awais Younus
spellingShingle	Awais Younus misc Q1-390 misc Interval-valued functions misc interval optimization misc KKT conditions misc gH -differentiability misc Fritz John conditions misc support vector machines misc Science (General) Interval-based KKT framework for support vector machines and beyond
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topic_title	Q1-390 Interval-based KKT framework for support vector machines and beyond Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines
topic	misc Q1-390 misc Interval-valued functions misc interval optimization misc KKT conditions misc gH -differentiability misc Fritz John conditions misc support vector machines misc Science (General)
topic_unstemmed	misc Q1-390 misc Interval-valued functions misc interval optimization misc KKT conditions misc gH -differentiability misc Fritz John conditions misc support vector machines misc Science (General)
topic_browse	misc Q1-390 misc Interval-valued functions misc interval optimization misc KKT conditions misc gH -differentiability misc Fritz John conditions misc support vector machines misc Science (General)
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title	Interval-based KKT framework for support vector machines and beyond
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title_full	Interval-based KKT framework for support vector machines and beyond
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title_sort	interval-based kkt framework for support vector machines and beyond
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title_auth	Interval-based KKT framework for support vector machines and beyond
abstract	Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results.
abstractGer	Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results.
abstract_unstemmed	Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush–Kuhn–Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results.
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title_short	Interval-based KKT framework for support vector machines and beyond
url	https://doi.org/10.1080/16583655.2024.2334017 https://doaj.org/article/13e4f07c3a614c65831a0f9ba2e8038f https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017 https://doaj.org/toc/1658-3655
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Interval-based KKT framework for support vector machines and beyond

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