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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017 |
| _version_ | 1797238937747456000 |
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| author | Awais Younus Rimsha Cemil Tunç |
| author_facet | Awais Younus Rimsha Cemil Tunç |
| author_sort | Awais Younus |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T17:43:35Z |
| format | Article |
| id | doaj.art-13e4f07c3a614c65831a0f9ba2e8038f |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-04-24T17:43:35Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-13e4f07c3a614c65831a0f9ba2e8038f2024-03-27T18:06:27ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552024-12-0118110.1080/16583655.2024.2334017Interval-based KKT framework for support vector machines and beyondAwais Younus0Rimsha1Cemil Tunç2CASPAM, Bahauddin Zakariya University, Multan, PakistanCASPAM, Bahauddin Zakariya University, Multan, PakistanDepartment of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, TurkeyOur 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.https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017Interval-valued functionsinterval optimizationKKT conditionsgH -differentiabilityFritz John conditionssupport vector machines |
| spellingShingle | Awais Younus Rimsha Cemil Tunç Interval-based KKT framework for support vector machines and beyond Journal of Taibah University for Science Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines |
| title | Interval-based KKT framework for support vector machines and beyond |
| title_full | Interval-based KKT framework for support vector machines and beyond |
| title_fullStr | Interval-based KKT framework for support vector machines and beyond |
| title_full_unstemmed | Interval-based KKT framework for support vector machines and beyond |
| title_short | Interval-based KKT framework for support vector machines and beyond |
| title_sort | interval based kkt framework for support vector machines and beyond |
| topic | Interval-valued functions interval optimization KKT conditions gH -differentiability Fritz John conditions support vector machines |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2024.2334017 |
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