Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints
In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and the generalized robust Slater constraint qualification (GRSCQ). These Karush-Kuhn-Tucker type...
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/11/1787 |
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| author | Rekha R. Jaichander Izhar Ahmad Krishna Kummari Suliman Al-Homidan |
| author_facet | Rekha R. Jaichander Izhar Ahmad Krishna Kummari Suliman Al-Homidan |
| author_sort | Rekha R. Jaichander |
| collection | DOAJ |
| description | In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and the generalized robust Slater constraint qualification (GRSCQ). These Karush-Kuhn-Tucker type robust necessary conditions are shown to be sufficient optimality conditions under generalized convexity. The Wolfe and Mond-Weir type robust dual problems are formulated over cones using generalized convexity assumptions, and usual duality results are established. The presented results are illustrated by non-trivial examples. |
| first_indexed | 2024-03-10T01:07:44Z |
| format | Article |
| id | doaj.art-c3f98e95e97c4ccaadc1e3cdeb57958c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:07:44Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c3f98e95e97c4ccaadc1e3cdeb57958c2023-11-23T14:24:31ZengMDPI AGMathematics2227-73902022-05-011011178710.3390/math10111787Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty ConstraintsRekha R. Jaichander0Izhar Ahmad1Krishna Kummari2Suliman Al-Homidan3Department of Mathematics, School of Science, GITAM-Hyderabad Campus, Hyderabad 502329, IndiaDepartment of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics, School of Science, GITAM-Hyderabad Campus, Hyderabad 502329, IndiaDepartment of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaIn this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and the generalized robust Slater constraint qualification (GRSCQ). These Karush-Kuhn-Tucker type robust necessary conditions are shown to be sufficient optimality conditions under generalized convexity. The Wolfe and Mond-Weir type robust dual problems are formulated over cones using generalized convexity assumptions, and usual duality results are established. The presented results are illustrated by non-trivial examples.https://www.mdpi.com/2227-7390/10/11/1787Generalized convexityrobust nonsmooth interval-valued optimization problemLU-optimal solutionoptimalityduality |
| spellingShingle | Rekha R. Jaichander Izhar Ahmad Krishna Kummari Suliman Al-Homidan Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints Mathematics Generalized convexity robust nonsmooth interval-valued optimization problem LU-optimal solution optimality duality |
| title | Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints |
| title_full | Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints |
| title_fullStr | Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints |
| title_full_unstemmed | Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints |
| title_short | Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints |
| title_sort | robust nonsmooth interval valued optimization problems involving uncertainty constraints |
| topic | Generalized convexity robust nonsmooth interval-valued optimization problem LU-optimal solution optimality duality |
| url | https://www.mdpi.com/2227-7390/10/11/1787 |
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