پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 675 |
| تعداد مقالات | 9,814 |
| تعداد مشاهده مقاله | 69,672,883 |
| تعداد دریافت فایل اصل مقاله | 49,025,819 |
Second-order optimization control problem for McKean-Vlasov systems via L-derivatives. | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 14، شماره 6، شهریور 2023، صفحه 1-22 اصل مقاله (532.59 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29043.4133 | ||
| نویسندگان | ||
| Naceur Rahmani1؛ Samira Boukaf2، 3؛ Mokhtar Hafayed* 4 | ||
| 1Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, PO Box 145, Biskra 7000, Algeria | ||
| 2Department of Mathematics, University Center Abdelhafid Boussouf, Mila, Algeria | ||
| 3Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, PO Box 145, Biskra 7000, Algeria | ||
| 4Laboratory of Mathematical Analysis, Probability and Optimizations, PO Box 145, University of Biskra, BISKRA, 7000 Algeria | ||
| تاریخ دریافت: 27 آذر 1401، تاریخ بازنگری: 24 اسفند 1401، تاریخ پذیرش: 03 اردیبهشت 1402 | ||
| چکیده | ||
| In this paper, we develop a second-order optimality condition for optimal regular-singular control in the integral form of McKean-Vlasov stochastic differential equations. The coefficients of the dynamic depend on the state process as well as on its probability law. The control process has two components, the first being regular and absolutely continuous and the second is an increasing process (componentwise), continuous on the left with limits on the right with bounded variation. The regular control variable is allowed to enter into both drift and diffusion coefficients. The control domain is assumed to be convex. Our main result is proved by applying the L-derivatives with respect to probability law. | ||
| کلیدواژهها | ||
| Second-order necessary conditions, Optimal stochastic control؛ L-derivatives with respect to measure؛ McKean-vlasov systems, Regular-singular control, Stochastic differential equation | ||
| مراجع | ||
|
[1] L.H.R. Alvarez, Singular stochastic control linear diffusion and optimal stopping: a class of solvable problems, SIAM J. Control Optim. 39 (2001), 1697–1710. [2] J.F. Bonnans and FJ. Silva, First and second order necessary conditions for stochastic optimal control problems, Appl. Math. Optim. 65 (2012), 403–439. [3] R. Buckdahn, J. Li, and J. Ma, A stochastic maximum principle for general mean-field system, Appl. Math. Optim. 74 (2016), 507–534. [4] R. Buckdahn, B. Djehiche, and J. Li. A general stochastic maximum principle for SDEs of mean-field type. Appl. Math. Optim. 64 (2011), 197–216. [5] A. Cadenillas and U. Haussman, The stochastic maximum principle for singular control problem, Stochastics: Int. J. Probab. Stochastic Proces. 49 (1994), no 3-4, 211–237. [6] P. Cardaliaguet, Notes on mean field games (from P.-L. Lions’ lectures at Coll`ege de France), Lecture Notes given at Tor Vergata, 2010. [7] R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics, Ann. Probab. 43 (2015), no. 5, 2647–2700. [8] R. Deepa and P. Muthukumar, Infinite horizon optimal control of mean-field delay system with semi-Markov modulated jump-diffusion processes, J. Anal. 27 (2019), 623–641. [9] Y. Dong and Q. Meng, Second-order necessary conditions for optimal control with recursive utilities, J. Optim. Theory Appl. 182 (2019), no. 2, 494–524. [10] F. Dufour and B. Miller, Necessary conditions for optimal singular stochastic control problems, Stochastics 79 (2007), no. 5, 469–504. [11] H. Frankowska, H. Zhang, and X. Zhang, First and second order necessary conditions for stochastic optimal controls, J. Differ. Equ. 262 (2017), no. 6, 3689–3736. [12] A. Ghoul, M. Hafayed, I.D Lakhdari, and S. Meherrem, Pointwise second-order necessary conditions for stochastic optimal control with jump diffusions, Commun. Math. Stat. (2022) https://doi.org/10.1007/s40304-021-00272-5. [13] M. Hafayed, S. Abbas, and A. Abba, On mean-field partial information maximum principle of optimal control for stochastic systems with Levy processes, J. Optim Theory Appl. 167 (2015), 1051–1069. [14] M. Hafayed, A. Abba, and S. Abbas, On partial-information optimal singular control problem for mean-field stochastic differential equations driven by Teugels martingales measures, Internat. J. Control 89 (2016), no. 2, 397–410. [15] M. Hafayed, A mean-field necessary and sufficient conditions for optimal singular stochastic control, Commun. Math. Stat. 1 (2014), no. 4, 417–435. [16] M. Hafayed, S. Boukaf, Y. Shi, and S. Meherrem, A McKean-Vlasov optimal mixed regular-singular control problem, for nonlinear stochastic systems with Poisson jump processes, Neurocomputing 182 (2016), no. 19, 133–144. [17] M. Hafayed, S. Meherrem, S. Eren, and D.H Guoclu, On optimal singular control problem for general McKean-Vlasov differential equations: Necessary and sufficient optimality conditions, Optim. Control Appl. Meth. 39 (2018), 1202–1219. [18] T. Hao and Q. Meng: A second-order maximum principle for singular optimal controls with recursive utilities of stochastic delay systems, Eur. J. Control 50 (2019), 96–106. [19] T. Hao, Q. Meng Singular optimal control problems with recursive utilities of mean-field type, Asian J. Control 23 (2021), no. 3, 1524–1535. [20] M. Huang, P. Caines, and R. Malhame, Large-population cost-coupled LQG problems with nonuniformagents: individual-mass behavior and decentralized ϵ-Nash equilibria, IEEE Trans. Automatic Control 52 (2007), 1560–1571. [21] S. Peng, A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim. 2 (1990), no. 4, 966–979. [22] H. Pham, Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications, Probab. Uncertain. Quant. Risk 1 (2016), no. 7, 1–26. [23] M. Kac, Foundations of kinetic theory, Proc. 3-rd Berkeley Sympos, Math. Statist. Prob. 3 (1956), 171–197. [24] J.M. Lasry, P.L, Lions, Mean-field games, Japan J. Math. 2 (2007), no. 1, 229–260. [25] P.L. Lions, Cours au College de France: Th`eorie des jeux a champ moyens, Audioconference (2012), 2006–2012. [26] H.P. McKean, A class of Markov processes associated with nonlinear parabolic equations, Proc. Natl. Acad. Sci. USA 56 (1966), 1907–1911. [27] Q. Meng and Y. Shen, Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach, J. Comput. Appl. Math. 279 (2015), 13–30. [28] G.Wang, C. Hang, and W. Zhang: Stochastic maximum principle for mean-field type optimal control under partial information, IEEE Trans. Automatic Control 59 (2014), no. 2, 522–528. [29] Y. Shen, Q. Meng, and P. Shi, Maximum principle for mean-field jump-diffusions to stochastic delay differential equations and its applications to finance, Automatica 50 (2014), 1565–1579. [30] S. Tang, A second-order maximum principle for singular optimal stochastic controls, Discrete Continuous Dyn.Syst. Ser. B. 14 (2010), no. 4, 1581–1599. [31] H. Zhang and X. Zhang, Pointwise second-order necessary conditions for stochastic optimal controls, Part I: The case of convex control constraint, SIAM J. Control Optim. (2015), no. 4, 2267–2296. [32] H. Zhang and X. Zhang, Pointwise second-order necessary conditions for stochastic optimal controls, part II: The general case, SIAM J. Control Optim. 55 (2017), no. 5, 2841–2875. | ||
|
آمار تعداد مشاهده مقاله: 16,647 تعداد دریافت فایل اصل مقاله: 8,188 |
||