Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 22
Number of page(s) 26
DOI https://doi.org/10.1051/cocv/2024003
Published online 04 April 2024
  1. W.M. Wonham, On a matrix Riccati equation of stochastic control. SIAM J. Control 6 (1968) 681–697. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.M. Bismut, Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14 (1976) 419–444. [Google Scholar]
  3. S. Chen, X. Li and X.Y. Zhou, Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim. 36 (1998) 1685–1702. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Ait Rami, J.B. Moore and X.Y. Zhou, Indefinite stochastic linear quadratic control and generalized differential Riccati equation. SIAM J. Control Optim. 40 (2002) 1296–1311. [Google Scholar]
  5. S. Tang, General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42 (2003) 53–75. [Google Scholar]
  6. S. Tang, Dynamic programming for general linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 53 (2015) 1082–1106. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Kohlmann and S. Tang, Multidimensional backward stochastic Riccati equations and applications. SIAM J. Control Optim. 41 (2003) 1696–1721. [Google Scholar]
  8. Y. Hu and X.Y. Zhou, Indefinite stochastic Riccati equations. SIAM J. Control Optim. 42 (2003) 123–137. [Google Scholar]
  9. J. Sun, X. Li and J. Yong, Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems. SIAM J. Control Optim. 54 (2016) 2274–2308. [Google Scholar]
  10. J. Sun, J. Xiong and J. Yong, Indefinite stochastic linear-quadratic optimal control problems with random coefficients: closed-loop representation of open-loop optimal controls. Ann. Appl. Probab. 31 (2021) 460–499. [Google Scholar]
  11. J. Sun and J. Yong, Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions. Springer, Cham (2019). [Google Scholar]
  12. Y. Hu and X.Y. Zhou, Constrained stochastic LQ control with random coefficients, and application to portfolio selection. SIAM J. Control Optim. 44 (2005) 444–466. [Google Scholar]
  13. X. Chen and X.Y. Zhou, Stochastic linear-quadratic control with conic control constraints on an infinite time horizon. SIAM J. Control Optim. 43 (2004) 1120–1150. [Google Scholar]
  14. Y. Hu, X. Shi and Z.Q. Xu, Constrained stochastic LQ control with regime switching and application to portfolio selection. Ann. Appl. Probab. 32 (2022) 426–460. [Google Scholar]
  15. Y. Hu, X. Shi and Z.Q. Xu, Constrained stochastic LQ control on infinite time horizon with regime switching. ESAIM Control Optim. Calc. Var. 28 (2022) 24. [Google Scholar]
  16. A.E.B. Lim and X.Y. Zhou, Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights, IEEE Trans. Automat. Control 44 (1999) 1359–1369. [Google Scholar]
  17. W. Wu, J. Gao, J.G. Lu and X. Li, On continuous-time constrained stochastic linear-quadratic control. Automatica 114 (2020) 6. [Google Scholar]
  18. X. Feng, Y. Hu and J. Huang, Backward Stackelberg differential game with constraints: a mixed terminal-perturbation and linear-quadratic approach. SIAM J. Control Optim. 60 (2022) 1488–1518. [Google Scholar]
  19. A.E.B. Lim, Quadratic hedging and mean-variance portfolio selection with random parameters in an incomplete market. Math. Oper. Res. 29 (2004) 132–161. [Google Scholar]
  20. H. Zhang and X.F. Zhang, Stochastic linear quadratic optimal control problems with expectation-type linear equality constraints on the terminal states. Syst. Control Lett. 177 (2023) 11. [Google Scholar]
  21. X. Bi, J. Sun and J. Xiong, Optimal control for controllable stochastic linear systems. ESAIM Control Optim. Calc. Var. 26 (2020) 23. [Google Scholar]
  22. B. Gashi, Stochastic minimum-energy control. Systems Control Lett. 85 (2015) 70–76. [Google Scholar]
  23. Y. Wang and C. Zhang, The norm optimal control problem for stochastic linear control systems. ESAIM Control Optim. Calc. Var. 21 (2015) 399–413. [Google Scholar]
  24. Y. Wang, D. Yang, J. Yong and Z. Yu, Exact controllability of linear stochastic differential equations and related problems. Math. Control Relat. Fields 7 (2017) 305–345. [Google Scholar]
  25. M.R. Hestenes, Multiplier and gradient methods. J. Optim. Theory Appl. 4 (1969) 303–320. [Google Scholar]
  26. M.J.D. Powell, A method for nonlinear constraints in minimization problems, in Optimization, edited by R. Fletcher. Academic Press, New York (1972). [Google Scholar]
  27. M. Bergounioux and K. Kunisch, Augmented Lagrangian techniques for elliptic state constrained optimal control problems. SIAM J. Control Optim. 35 (1997) 1524–1543. [Google Scholar]
  28. M. Fortin and R. Glowinski, Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary Value Problems. North-Holland Publishing Co., Amsterdam (1983). [Google Scholar]
  29. K. Ito and K. Kunisch, The augmented Lagrangian method for equality and inequality constraints in Hilbert spaces. Math. Program. 46 (1990) 341–360. [Google Scholar]
  30. L. Pfeiffer, Optimality conditions in variational form for non-linear constrained stochastic control problems. Math. Control Relat. Fields 10 (2020) 493–526. [Google Scholar]
  31. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer, New York (2000). [Google Scholar]
  32. A.L. Dontchev and R.T. Rockafellar, Implicit Functions and Solution Mappings: A View from Variational Analysis, Second edition. Springer, New York (2014). [Google Scholar]
  33. S. Peng, Backward stochastic differential equation and exact controllability of stochastic control systems. Prog. Nat. Sci. 4 (1994) 274–284. [Google Scholar]
  34. Q. Lü and X. Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations. Springer, Cham (2021). [Google Scholar]
  35. J. Yong and X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer, New York (1999). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.