메뉴 건너뛰기




Volumn 65, Issue 3, 2012, Pages 403-439

First and second order necessary conditions for stochastic optimal control problems

Author keywords

Final state constraints; First and second order optimality conditions; Polyhedric constraints; Stochastic optimal control; Variational approach

Indexed keywords

FINAL STATE CONSTRAINTS; POLYHEDRIC CONSTRAINTS; SECOND-ORDER OPTIMALITY CONDITIONS; STOCHASTIC OPTIMAL CONTROL; VARIATIONAL APPROACHES;

EID: 84867252057     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-012-9162-4     Document Type: Article
Times cited : (52)

References (32)
  • 1
    • 0002660254 scopus 로고
    • Lectures on stochastic control
    • Springer, Berlin
    • Bensoussan, A.: Lectures on Stochastic Control. Lecture Notes in Math., vol. 972. Springer, Berlin (1981)
    • (1981) Lecture notes in math , vol.972
    • Bensoussan, A.1
  • 2
    • 0020752016 scopus 로고
    • Stochastic maximum principle for distributed parameter system
    • Bensoussan, A.: Stochastic maximum principle for distributed parameter system. J. Franklin Inst. 315, 387-406 (1983)
    • (1983) J. Franklin Inst , vol.315 , pp. 387-406
    • Bensoussan, A.1
  • 4
    • 0343620817 scopus 로고
    • Théorie probabiliste du contrôle des diffusions
    • Bismut, J.M.: Théorie probabiliste du contrôle des diffusions. Mem. Am. Math. Soc. 4, 1-130 (1976)
    • (1976) Mem. Am. Math. Soc , vol.4 , pp. 1-130
    • Bismut, J.M.1
  • 5
    • 0003001464 scopus 로고
    • An introductory approach to duality in optimal stochastic control
    • Bismut, J.M.: An introductory approach to duality in optimal stochastic control. SIAM Rev. 20, 62-78 (1978)
    • (1978) SIAM Rev , vol.20 , pp. 62-78
    • Bismut, J.M.1
  • 6
    • 0021587924 scopus 로고
    • On the choice of the function spaces for some state-constrained control problems
    • Bonnans, J.F., Casas, E.: On the choice of the function spaces for some state-constrained control problems. Numer. Funct. Anal. Optim. 7(4), 333-348 (1984)
    • (1984) Numer. Funct. Anal. Optim , vol.7 , Issue.4 , pp. 333-348
    • Bonnans, J.F.1    Casas, E.2
  • 8
    • 0029271717 scopus 로고
    • The stochastic maximum principle for linear convex optimal control with random coefficients
    • Cadenillas, A., Karatzas, I.: The stochastic maximum principle for linear convex optimal control with random coefficients. SIAM J. Control Optim. 33, 590-624 (1995)
    • (1995) SIAM J. Control Optim , vol.33 , pp. 590-624
    • Cadenillas, A.1    Karatzas, I.2
  • 9
    • 62449107325 scopus 로고    scopus 로고
    • Jacobi type conditions for singular extremals
    • Dmitruk, A.V.: Jacobi type conditions for singular extremals. Control Cybern. 37, 285-306 (2008)
    • (2008) Control Cybern , vol.37 , pp. 285-306
    • Dmitruk, A.V.1
  • 10
    • 0347771653 scopus 로고    scopus 로고
    • The Graves theorem revisited
    • Dontchev, A.L.: The Graves theorem revisited. J. Convex Anal. 3(1), 45-53 (1996)
    • (1996) J. Convex Anal , vol.3 , Issue.1 , pp. 45-53
    • Dontchev, A.L.1
  • 12
    • 84972539529 scopus 로고
    • Some mapping theorems
    • Graves, L.M.: Some mapping theorems. Duke Math. J. 17, 111-114 (1950)
    • (1950) Duke Math. J , vol.17 , pp. 111-114
    • Graves, L.M.1
  • 14
    • 0007211052 scopus 로고
    • General necessary conditions for optimal control of stochastic systems
    • Haussmann, U.G.: General necessary conditions for optimal control of stochastic systems. Math. Program. Stud. 6, 34-48 (1976)
    • (1976) Math. Program. Stud , vol.6 , pp. 34-48
    • Haussmann, U.G.1
  • 15
    • 0001517850 scopus 로고
    • Some examples of optimal stochastic controls or: The stochastic maximum principle at work
    • Haussmann, U.G.: Some examples of optimal stochastic controls or: the stochastic maximum principle at work. SIAM Rev. 23, 292-307 (1981)
    • (1981) SIAM Rev , vol.23 , pp. 292-307
    • Haussmann, U.G.1
  • 16
    • 84972487915 scopus 로고
    • Applications of the theory of quadratic forms in Hilbert space to the calculus of variations
    • Hestenes, M.R.: Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pac. J. Math. 1, 525-581 (1951)
    • (1951) Pac. J. Math , vol.1 , pp. 525-581
    • Hestenes, M.R.1
  • 19
    • 84867238942 scopus 로고
    • On the existence of optimal stochastic controls
    • Kushner, H.J.: On the existence of optimal stochastic controls. J.Math. Anal. Appl. 3, 463-474 (1965)
    • (1965) J.Math. Anal. Appl , vol.3 , pp. 463-474
    • Kushner, H.J.1
  • 20
    • 0347202481 scopus 로고
    • On the stochastic maximum principle: Fixed time of control
    • Kushner, H.J.: On the stochastic maximum principle: Fixed time of control. J. Math. Anal. Appl. 11, 78-92 (1965)
    • (1965) J. Math. Anal. Appl , vol.11 , pp. 78-92
    • Kushner, H.J.1
  • 21
    • 0001186380 scopus 로고
    • Necessary conditions for continuous parameter stochastic optimization problems
    • Kushner, H.J.: Necessary conditions for continuous parameter stochastic optimization problems. SIAM J. Control Optim. 10, 550-565 (1972)
    • (1972) SIAM J. Control Optim , vol.10 , pp. 550-565
    • Kushner, H.J.1
  • 22
    • 84947513018 scopus 로고
    • Optimal control of diffusion processes and hamilton-jacobi-bellman equations
    • I. The dynamic programming principle and applications
    • Lions, P.-L.: Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications. Commun. Partial Differ. Equ. 8(10), 1101-1174 (1983)
    • (1983) Commun. Partial Differ. Equ , vol.8 , Issue.10 , pp. 1101-1174
    • Lions, P.-L.1
  • 23
    • 84947513018 scopus 로고
    • Optimal control of diffusion processes and hamilton-jacobi-bellman equations
    • Part 2: Viscosity solutions and uniqueness
    • Lions, P.-L.: Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part 2: viscosity solutions and uniqueness. Commun. Partial Differ. Equ. 8, 1229-1276 (1983)
    • (1983) Commun. Partial Differ. Equ , vol.8 , pp. 1229-1276
    • Lions, P.-L.1
  • 24
    • 49949133603 scopus 로고
    • The Fritz-John necessary optimality conditions in the presence of equality and inequality constraints
    • Mangasarian, O., Fromovitz, S.: The Fritz-John necessary optimality conditions in the presence of equality and inequality constraints. J. Math. Anal. Appl. 7, 37-47 (1967)
    • (1967) J. Math. Anal. Appl , vol.7 , pp. 37-47
    • Mangasarian, O.1    Fromovitz, S.2
  • 25
    • 0041919113 scopus 로고
    • Contrôle dans les inéquations variationnelles
    • Mignot, F.: Contrôle dans les inéquations variationnelles. J. Funct. Anal. 22, 25-39 (1976)
    • (1976) J. Funct. Anal , vol.22 , pp. 25-39
    • Mignot, F.1
  • 26
    • 49649090400 scopus 로고    scopus 로고
    • A variational formula for stochastic controls and some applications
    • Mou, L., Yong, J.: A variational formula for stochastic controls and some applications. Pure Appl. Math. Q. 3, 539-567 (2007)
    • (2007) Pure Appl. Math. Q , vol.3 , pp. 539-567
    • Mou, L.1    Yong, J.2
  • 27
    • 0025462369 scopus 로고
    • A general stochastic maximum principle for optimal control problems
    • Peng, S.: A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28, 966-979 (1990)
    • (1990) SIAM J. Control Optim , vol.28 , pp. 966-979
    • Peng, S.1
  • 28
    • 70450189702 scopus 로고    scopus 로고
    • Optimisation et contrôle stochastique appliqués à la finance
    • Springer, Berlin
    • Pham, H.: Optimisation et contrôle stochastique appliqués à la finance. Mathématiques & Applications, vol. 61. Springer, Berlin (2007)
    • (2007) Mathématiques & Applications , vol.61
    • Pham, H.1
  • 31
    • 0348196100 scopus 로고
    • The connection between the maximum principle and dynamic programming in stochastic control
    • Zhou, X.Y.: The connection between the maximum principle and dynamic programming in stochastic control. Stoch. Stoch. Rep. 31, 1-13 (1990)
    • (1990) Stoch. Stoch. Rep , vol.31 , pp. 1-13
    • Zhou, X.Y.1
  • 32
    • 0000278406 scopus 로고
    • A unified treatment of maximum principle and dynamic programming in stochastic controls
    • Zhou, X.Y.: A unified treatment of maximum principle and dynamic programming in stochastic controls. Stoch. Stoch. Rep. 36, 137-161 (1991)
    • (1991) Stoch. Stoch. Rep , vol.36 , pp. 137-161
    • Zhou, X.Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.