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Sufficiency and duality of multi-objective bi-level programming problem under Guignard constraint qualification |
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| รหัสดีโอไอ | |
| Creator | Navdeep Kailey |
| Title | Sufficiency and duality of multi-objective bi-level programming problem under Guignard constraint qualification |
| Contributor | Shivani Saini |
| Publisher | Maejo University |
| Publication Year | 2565 |
| Journal Title | Maejo International Journal of Science and Technology |
| Journal Vol. | 16 |
| Journal No. | 1 |
| Page no. | 13 |
| Keyword | bi-level programming, sufficient optimality conditions, Clarke sub-differential, convexifactors, Mond-Weir dual |
| Website title | Maejo International Journal of Science and Technology |
| ISSN | 1905-7873 |
| Abstract | Although a great deal of work has been done on bi-level programming problems (BPPs) during the last few decades, there is still a substantial gap in the literature on sufficient optimality conditions and duality results of BPPs. This article aims to develop sufficient optimality conditions and Mond-Weir-type dual for a multi-objective BPP from an optimistic perspective under the Guignard constraint qualification. Using the weighted sum scalarisation at the lower level and a special function at the upper level, we convert the multi-objective BPP to the corresponding single-objective BPP. With the help of optimal value reformulation, we reformulate the single-objective BPP as a single-level mathematical programming problem. Using the generalised convexity, we develop sufficient optimality conditions. Moreover, we formulate Mond-Weir type dual and establish the corresponding duality results. |
