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Optimization problems with nonconvex multiobjective generalized Nash equilibrium problem constraints | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 خرداد 1403 اصل مقاله (507.45 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29435.1993 | ||
| نویسندگان | ||
| El-yahyaoui youness* 1؛ Lahoussine Lafhim2 | ||
| 1Laboratory LASMA, Department of mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco | ||
| 2Laboratory LASMA, Department of mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco | ||
| چکیده | ||
| This work discusses a category of optimization problems in which the lower-level problems include multiobjective generalized Nash equilibrium problems. Despite the fact that it has various possible applications, there has been little research into it in the literature. We provide a single-level reformulation for these types of problems and highlight their equivalence in terms of global and local minimizers. Our method consists of transforming our problem into a one-level optimization problem, utilizing the kth-objective weighted-constraint and optimal value reformulation. The Mordukhovich generalized differentiation calculus is then used to derive completely detailed first-order necessary optimality conditions in the smooth setting. | ||
| کلیدواژه‌ها | ||
| Mathematical programming؛ generalized Nash equilibrium problem؛ kth-objective weighted-constraint approach؛ optimal value function؛ optimality conditions | ||
| مراجع | ||
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[1] M.J. Alves and C.H. Antunes, A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing, Comput. Oper. Res. 92 (2018), 130–144. https://doi.org/10.1016/j.cor.2017.12.014 [2] J.F. Bard, Practical Bilevel Optimization: Algorithms and Applications, Springer Science & Business Media, New York, 2013.
[3] H. Bonnel, Optimality conditions for the semivectorial bilevel optimization problem, Pac. J. Optim. 2 (2006), no. 3, 447–467.
[4] H. Bonnel and J. Morgan, Semivectorial bilevel optimization problem: penalty approach, J. Optim. Theory Appl. 131 (2006), no. 3, 365–382. https://doi.org/10.1007/s10957-006-9150-4 [5] H. Bonnel and J. Morgan, Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems, Computational and Analytical Mathematics (New York, NY) (D.H. Bailey, H.H. Bauschke, P. Borwein, F. Garvan, M. Th´era, J.D. Vanderwerff, and H. Wolkowicz, eds.), Springer New York, 2013, pp. 45–78.
[6] R.S. Burachik, C.Y. Kaya, and M.M. Rizvi, A new scalarization technique to approximate pareto fronts of problems with disconnected feasible sets, J. Optim. Theory Appl. 162 (2014), no. 2, 428–446. https://doi.org/10.1007/s10957-013-0346-0 [7] S. Dempe, Foundations of Bilevel Programming, Springer Science & Business Media, New York, 2002.
[8] S. Dempe, B.S. Mordukhovich, and A.B. Zemkoho, Sensitivity analysis for two-level value functions with applications to bilevel programming, SIAM J. Optim. 22 (2012), no. 4, 1309–1343. https://doi.org/10.1137/110845197 [9] S. Dempe, B.S. Mordukhovich, and A.B. Zemkoho, Necessary optimality conditions in pessimistic bilevel programming, Optimization 63 (2014), no. 4, 505–533. https://doi.org/10.1080/02331934.2012.696641 [10] S. Dempe and A.B. Zemkoho, The generalized mangasarian-fromowitz constraint qualification and optimality conditions for bilevel programs, J. Optim. Theory Appl. 148 (2011), no. 1, 46–68. https://doi.org/10.1007/s10957-010-9744-8 [11] M. Ehrgott, Multicriteria Optimization, Springer Science & Business Media, Berlin, 2005.
[12] L. Guo, Mathematical programs with multiobjective generalized nash equilibrium problems in the constraints, Oper. Res. Lett. 49 (2021), no. 1, 11–16. https://doi.org/10.1016/j.orl.2020.11.001 [13] R. Henrion, A. Jourani, and J. Outrata, On the calmness of a class of multifunctions, SIAM J. Optim. 13 (2002), no. 2, 603–618. https://doi.org/10.1137/S1052623401395553 [14] J. Jahn, Vector Optimization, Springer, Berlin, 2009.
[15] L. Lafhim, New optimality conditions and a scalarization approach for a nonconvex semi-vectorial bilevel optimization problem, Positivity 24 (2020), no. 2, 395–413. https://doi.org/10.1007/s11117-019-00685-1 [16] L. Lafhim, First-and second-order optimality conditions in optimistic bilevel setvalued programming, Optimization 71 (2022), no. 7, 1955–1981. https://doi.org/10.1080/02331934.2020.1846189 [17] L. Lafhim and A. Zemkoho, Extension of the value function reformulation to multiobjective bilevel optimization, Optim. Lett. 17 (2023), no. 6, 1337–1358. https://doi.org/10.1007/s11590-022-01948-9 [18] B.S. Mordukhovich, Variational Analysis and Generalized Differentiation I: Basic Theory, Springer, Berlin, 2006.
[19] B.S. Mordukhovich, Variational Analysis and Generalized Differentiation II: Applications, Springer, Berlin, 2006.
[20] B.S. Mordukhovich and N.M. Nam, Variational stability and marginal functions via generalized differentiation, Math. Oper. Res. 30 (2005), no. 4, 800–816. https://doi.org/10.1287/moor.1050.0147 [21] B.S. Mordukhovich, N.M. Nam, and N.D. Yen, Subgradients of marginal functions in parametric mathematical programming, Math. Program. 116 (2009), no. 1, 369–396. https://doi.org/10.1007/s10107-007-0120-x [22] R.T. Rockafellar and R.J.B. Wets, Variational Analysis, Springer Science & Business Media, Berlin, 2009.
[23] L. Samuelson, Game theory in economics and beyond, J. Econ. Perspect. 30 (2016), no. 4, 107–130.
[24] J.M. Smith, Game theory and the evolution of behaviour, Behav. Brain Res. 7 (1984), no. 1, 95–101. https://doi.org/10.1017/S0140525X00026327 [25] L. Sun, Equivalent bilevel programming form for the generalized nash equilibrium problem, J. Math. Res. 2 (2010), no. 1, 8–13.
[26] E.Y. Youness and L. Lahoussine, Necessary optimality conditions for a semivectorial bilevel optimization problem via a revisited charnes–cooper scalarization, Optimization (2023), In press. https://doi.org/10.1080/02331934.2023.2249916 | ||
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