PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS
We employ some advanced tools of variational analysis and generalised differentiation such as the nonsmooth version of Fermat's rule, the limiting sub-differential of maximum functions, and the sum rules for the Frechet and Mordukhovich sub-differentials to establish necessary conditions for (l...
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| Format: | Article |
| Language: | English |
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Dalat University
2012-06-01
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| Series: | Tạp chí Khoa học Đại học Đà Lạt |
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| Online Access: | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/193 |
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| author | Thái Doãn Chương |
| author_facet | Thái Doãn Chương |
| author_sort | Thái Doãn Chương |
| collection | DOAJ |
| description | We employ some advanced tools of variational analysis and generalised differentiation such as the nonsmooth version of Fermat's rule, the limiting sub-differential of maximum functions, and the sum rules for the Frechet and Mordukhovich sub-differentials to establish necessary conditions for (local) properly efficient solutions and (local) isolated minimizers of a multi-objective optimisation problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions are also supplied under assumptions of (local) convex/affine functions or L-invex-infine functions defined in terms of the limiting sub-differential of locally Lipschitz functions. In addition, we propose a type of Wolfe dual problem and explore weak/strong duality relations under L-invexity-infineness hypotheses. |
| format | Article |
| id | doaj-art-bcfca851ea944de4bc5b14e6a6a66140 |
| institution | Kabale University |
| issn | 0866-787X |
| language | English |
| publishDate | 2012-06-01 |
| publisher | Dalat University |
| record_format | Article |
| series | Tạp chí Khoa học Đại học Đà Lạt |
| spelling | doaj-art-bcfca851ea944de4bc5b14e6a6a661402025-02-02T01:37:31ZengDalat UniversityTạp chí Khoa học Đại học Đà Lạt0866-787X2012-06-012210.37569/DalatUniversity.2.2.193(2012)PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMSThái Doãn Chương0Department of Mathematics and Applications, Saigon UniversityWe employ some advanced tools of variational analysis and generalised differentiation such as the nonsmooth version of Fermat's rule, the limiting sub-differential of maximum functions, and the sum rules for the Frechet and Mordukhovich sub-differentials to establish necessary conditions for (local) properly efficient solutions and (local) isolated minimizers of a multi-objective optimisation problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions are also supplied under assumptions of (local) convex/affine functions or L-invex-infine functions defined in terms of the limiting sub-differential of locally Lipschitz functions. In addition, we propose a type of Wolfe dual problem and explore weak/strong duality relations under L-invexity-infineness hypotheses.https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/193Optimality conditionDualityIsolated minimizerMordukhovich sub-differentialL-invex-infine functionMulti-objective optimisation |
| spellingShingle | Thái Doãn Chương PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS Tạp chí Khoa học Đại học Đà Lạt Optimality condition Duality Isolated minimizer Mordukhovich sub-differential L-invex-infine function Multi-objective optimisation |
| title | PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS |
| title_full | PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS |
| title_fullStr | PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS |
| title_full_unstemmed | PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS |
| title_short | PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS |
| title_sort | proper and isolated efficiencies in multiobjective optimization problems |
| topic | Optimality condition Duality Isolated minimizer Mordukhovich sub-differential L-invex-infine function Multi-objective optimisation |
| url | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/193 |
| work_keys_str_mv | AT thaidoanchuong properandisolatedefficienciesinmultiobjectiveoptimizationproblems |