آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 116 |
| تعداد مقالات | 1,347 |
| تعداد مشاهده مقاله | 1,352,373 |
| تعداد دریافت فایل اصل مقاله | 1,293,418 |
Bilevel vector variational inequalities and multiobjective bilevel optimization problems | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 فروردین 1404 اصل مقاله (420.37 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29874.2200 | ||
| نویسندگان | ||
| Mohsine Jennane* 1؛ El Mostafa Kalmoun2 | ||
| 1FSDM, Department of mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco | ||
| 2School of Science and Engineering, Al Akhawayn University in Ifrane, PO Box 104, Ifrane, 53000, Morocco | ||
| چکیده | ||
| In this paper, we introduce the concepts of bilevel vector variational inequalities (BVVI) of both Minty and Stampacchia types. Additionally, we establish connections between BVVI and multiobjective bilevel optimization problems (MBOP), focusing on the use of tangential subdifferentials. We investigate the relationship between the vector efficient points of MBOP and the solutions of BVVI, particularly under conditions of generalized convexity. | ||
| کلیدواژه‌ها | ||
| Multiobjective bilevel optimization؛ bilevel vector variational inequalities؛ tangential subdifferential؛ generalized convexity؛ monotonicity | ||
| مراجع | ||
|
[1] S. Al-Homidan and Q.H. Ansari, Generalized minty vector variational-like inequalities and vector optimization problems, J. Optim. Theory Appl. 144 (2010), no. 1, 1–11. https://doi.org/10.1007/s10957-009-9591-7
[2] F.H. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1990.
[3] S. Dempe, First-order necessary optimality conditions for general bilevel programming problems, J. Optim. Theory Appl. 95 (1997), no. 3, 735–739. https://doi.org/10.1023/A:1022646611097
[4] A. Fischer, A.B. Zemkoho, and S. Zhou, Semismooth newton-type method for bilevel optimization: global convergence and extensive numerical experiments, Optim. Methods Softw. 37 (2022), no. 5, 1770–1804. https://doi.org/10.1080/10556788.2021.1977810
[5] F. Giannessi, Theorems of the alternative: quadratic programs and complementarity problems, pp. 151–186, John Wiley & Sons Ltd, New York, 1980.
[6] P. Gupta and S.K. Mishra, On minty variational principle for nonsmooth vector optimization problems with generalized approximate convexity, Optimization 67 (2018), no. 8, 1157–1167. https://doi.org/10.1080/02331934.2018.1466884
[7] H. Huang, Strict vector variational inequalities and strict Pareto efficiency in nonconvex vector optimization, Positivity 19 (2015), no. 1, 95–109. https://doi.org/10.1007/s11117-014-0285-5
[8] M. Jennane, L. El Fadil, and E.M. Kalmoun, On local quasi efficient solutions for nonsmooth vector optimization problems, Croat. Oper. Res. Rev. 11 (2020), no. 1, 1–10. https://doi.org/10.17535/crorr.2020.0001
[9] M. Jennane, E.M. Kalmoun, and L. El Fadil, Optimality conditions for nonsmooth multiobjective bilevel optimization using tangential subdifferentials, RAIRO Oper. Res. 55 (2021), no. 5, 3041–3048. https://doi.org/10.1051/ro/2021139
[10] B. Kohli, Variational inequalities and optimistic bilevel programming problem via convexifactors, pp. 243–255, Springer New York, New York, NY, 2011.
[11] V. Laha and S.K. Mishra, On vector optimization problems and vector variational inequalities using convexificators, Optimization 66 (2017), no. 11, 1837–1850. https://doi.org/10.1080/02331934.2016.1250268
[12] C. Lemaréchal, An introduction to the theory of nonsmooth optimization, Optimization 17 (1986), no. 6, 827–858. https://doi.org/10.1080/02331938608843204 [13] J.E. Martínez-Legaz, Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints, Optim. Lett. 9 (2015), no. 5, 1017–1023. https://doi.org/10.1007/s11590-014-0822-y
[14] J.E. Martínez-Legaz, A mean value theorem for tangentially convex functions, Set-Valued Var. Anal. 31 (2023), no. 2, Article numbe 13. https://doi.org/10.1007/s11228-023-00674-3
[15] P. Michel and J.P. Penot, A generalized derivative for calm and stable functions, Diff. Integ. Eq. 5 (1992), no. 2, 433–454.
[16] S.K. Mishra and V. Laha, On minty variational principle for nonsmooth vector optimization problems with approximate convexity, Optim. Lett. 10 (2016), no. 3, 577–589. https://doi.org/10.1007/s11590-015-0883-6
[17] J.V. Outrata, On the numerical solution of a class of Stackelberg problems, Zeitschrift für Operations Research 34 (1990), no. 4, 255–277. https://doi.org/10.1007/BF01416737
[18] B.N. Pshenichnyi, Necessary Conditions for an Extremum, CRC Press, 2020.
[19] G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences 258 (1964), no. 18, 4413.
[20] S.K. Suneja and B. Kohli, Optimality and duality results for bilevel programming problem using convexifactors, J. Optim. Theory Appl. 150 (2011), no. 1, 1–19. https://doi.org/10.1007/s10957-011-9819-1
[21] J.J. Ye and D.L. Zhu, Optimality conditions for bilevel programming problems, Optimization 33 (1995), no. 1, 9–27. https://doi.org/10.1080/02331939508844060 [22] A. Yezza, First-order necessary optimality conditions for general bilevel programming problems, J. Optim. Theory Appl. 89 (1996), no. 1, 189–219. https://doi.org/10.1007/BF02192648
[23] A.B. Zemkoho and S. Zhou, Theoretical and numerical comparison of the Karush–Kuhn–Tucker and value function reformulations in bilevel optimization, Comput. Optim. Appl. 78 (2021), no. 2, 625–674. https://doi.org/10.1007/s10589-020-00250-7 | ||
|
آمار تعداد مشاهده مقاله: 72 تعداد دریافت فایل اصل مقاله: 68 |
||