Mixed-type duality approach for interval-valued programming problems with vanishing constraints
In this article, we present a new mixed-type dual problem for the challenging class of the interval-valued optimization problem with vanishing constraints. The introduced dual problem does not directly include the index set, but it still requires calculations related to index sets, which makes it ch...
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Elsevier
2025-03-01
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| Series: | Results in Control and Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S266672072500013X |
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| author | Vivek Singh Neelima Shekhawat |
| author_facet | Vivek Singh Neelima Shekhawat |
| author_sort | Vivek Singh |
| collection | DOAJ |
| description | In this article, we present a new mixed-type dual problem for the challenging class of the interval-valued optimization problem with vanishing constraints. The introduced dual problem does not directly include the index set, but it still requires calculations related to index sets, which makes it challenging to address these models from an algorithm perspective. The relationship between the original interval-valued programming problem with vanishing constraints and its mixed-type dual are discussed by weak, strong and strict converse duality theorems using the assumption of generalized convexity. We also present a non-trivial example to illustrate the theoretical aspects. Our proposed interval-valued mixed-type dual technique unifies the dual techniques discussed in Hu et al. (2020). |
| format | Article |
| id | doaj-art-0613a37ce04f497288e0f170abfce6f2 |
| institution | Kabale University |
| issn | 2666-7207 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj-art-0613a37ce04f497288e0f170abfce6f22025-01-28T04:14:56ZengElsevierResults in Control and Optimization2666-72072025-03-0118100527Mixed-type duality approach for interval-valued programming problems with vanishing constraintsVivek Singh0Neelima Shekhawat1Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, IndiaCorresponding author.; Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, IndiaIn this article, we present a new mixed-type dual problem for the challenging class of the interval-valued optimization problem with vanishing constraints. The introduced dual problem does not directly include the index set, but it still requires calculations related to index sets, which makes it challenging to address these models from an algorithm perspective. The relationship between the original interval-valued programming problem with vanishing constraints and its mixed-type dual are discussed by weak, strong and strict converse duality theorems using the assumption of generalized convexity. We also present a non-trivial example to illustrate the theoretical aspects. Our proposed interval-valued mixed-type dual technique unifies the dual techniques discussed in Hu et al. (2020).http://www.sciencedirect.com/science/article/pii/S266672072500013XInterval-valued programming problemVanishing constraintsUnified duality |
| spellingShingle | Vivek Singh Neelima Shekhawat Mixed-type duality approach for interval-valued programming problems with vanishing constraints Results in Control and Optimization Interval-valued programming problem Vanishing constraints Unified duality |
| title | Mixed-type duality approach for interval-valued programming problems with vanishing constraints |
| title_full | Mixed-type duality approach for interval-valued programming problems with vanishing constraints |
| title_fullStr | Mixed-type duality approach for interval-valued programming problems with vanishing constraints |
| title_full_unstemmed | Mixed-type duality approach for interval-valued programming problems with vanishing constraints |
| title_short | Mixed-type duality approach for interval-valued programming problems with vanishing constraints |
| title_sort | mixed type duality approach for interval valued programming problems with vanishing constraints |
| topic | Interval-valued programming problem Vanishing constraints Unified duality |
| url | http://www.sciencedirect.com/science/article/pii/S266672072500013X |
| work_keys_str_mv | AT viveksingh mixedtypedualityapproachforintervalvaluedprogrammingproblemswithvanishingconstraints AT neelimashekhawat mixedtypedualityapproachforintervalvaluedprogrammingproblemswithvanishingconstraints |