메뉴 건너뛰기




Volumn 50, Issue 3, 2003, Pages 221-228

Semi-smooth Newton methods for state-constrained optimal control problems

Author keywords

Augmented Lagrangians; Semi smooth Newton methods; State constrained optimal control; Superlinear convergence

Indexed keywords

LAGRANGE MULTIPLIERS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0141793144     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(03)00156-7     Document Type: Article
Times cited : (112)

References (20)
  • 1
    • 0141561055 scopus 로고
    • Convergence of finite element approximations to state constrained convex arabolic boundary control problems
    • Alt W., Mackenroth U. Convergence of finite element approximations to state constrained convex arabolic boundary control problems. SIAM J. Control Optim. 22:1991;83-98.
    • (1991) SIAM J. Control Optim. , vol.22 , pp. 83-98
    • Alt, W.1    Mackenroth, U.2
  • 2
    • 0001018402 scopus 로고    scopus 로고
    • State-constrained relaxed problems for semilinear elliptic equations
    • Arada N., Raymond J.P. State-constrained relaxed problems for semilinear elliptic equations. J. Math. Anal. Appl. 223:1998;248-271.
    • (1998) J. Math. Anal. Appl. , vol.223 , pp. 248-271
    • Arada, N.1    Raymond, J.P.2
  • 5
    • 84963483361 scopus 로고
    • On boundary state constrained control problems
    • Bergounioux M. On boundary state constrained control problems. Numer. Funct. Anal. Optim. 14:1993;515-543.
    • (1993) Numer. Funct. Anal. Optim. , vol.14 , pp. 515-543
    • Bergounioux, M.1
  • 6
    • 0027659335 scopus 로고
    • Augmented Lagrangian method for distributed optimal control problems with state constraints
    • Bergounioux M. Augmented Lagrangian method for distributed optimal control problems with state constraints. J. Optim. Theory Appl. 78:1993;493-521.
    • (1993) J. Optim. Theory Appl. , vol.78 , pp. 493-521
    • Bergounioux, M.1
  • 7
    • 0034353740 scopus 로고    scopus 로고
    • A comparison of a Moreau-Yosida based active set strategy and interior point problems for constrained optimal control problems
    • Bergounioux M., Haddou M., Hintermüller M., Kunisch K. A comparison of a Moreau-Yosida based active set strategy and interior point problems for constrained optimal control problems. SIAM J. Optim. 11:2000;495-521.
    • (2000) SIAM J. Optim. , vol.11 , pp. 495-521
    • Bergounioux, M.1    Haddou, M.2    Hintermüller, M.3    Kunisch, K.4
  • 8
    • 0037445081 scopus 로고    scopus 로고
    • On the structure of Lagrange multipliers for state-constrained optimal control problems
    • Bergounioux M., Kunisch K. On the structure of Lagrange multipliers for state-constrained optimal control problems. Systems Control Lett. 48:2002;169-176.
    • (2002) Systems Control Lett. , vol.48 , pp. 169-176
    • Bergounioux, M.1    Kunisch, K.2
  • 9
    • 0001654425 scopus 로고
    • An extension of Pontryagin's maximum principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities
    • Bonnans F.J., Casas E. An extension of Pontryagin's maximum principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities. SIAM J. Control Optim. 33:1995;274-298.
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 274-298
    • Bonnans, F.J.1    Casas, E.2
  • 10
    • 0027623859 scopus 로고
    • Boundary control of semilinear elliptic equations with pointwise state constraints
    • Casas E. Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31:1993;993-1006.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 993-1006
    • Casas, E.1
  • 11
    • 0141449515 scopus 로고    scopus 로고
    • Second order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations
    • to appear
    • E. Casas, F. Tröltzsch, Second order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations, Appl. Math. Optim., to appear.
    • Appl. Math. Optim.
    • Casas, E.1    Tröltzsch, F.2
  • 12
    • 0038587058 scopus 로고    scopus 로고
    • Second order sufficient optimality conditions for nonlinear elliptic control problems
    • Casas E., Tröltzsch F., Unger A. Second order sufficient optimality conditions for nonlinear elliptic control problems. J. Anal. Appl. 15:1996;687-707.
    • (1996) J. Anal. Appl. , vol.15 , pp. 687-707
    • Casas, E.1    Tröltzsch, F.2    Unger, A.3
  • 13
    • 0041657515 scopus 로고    scopus 로고
    • The primal-dual active set strategy as semi-smooth Newton method
    • Hintermüller M., Ito K., Kunisch K. The primal-dual active set strategy as semi-smooth Newton method. SIAM J. Optim. 13:2002;865-888.
    • (2002) SIAM J. Optim. , vol.13 , pp. 865-888
    • Hintermüller, M.1    Ito, K.2    Kunisch, K.3
  • 14
    • 4244016718 scopus 로고    scopus 로고
    • A level set approach for the solution of a state-constrained optimal control problem
    • to appear
    • M. Hintermüller, W. Ring, A level set approach for the solution of a state-constrained optimal control problem, Numer. Math., to appear.
    • Numer. Math.
    • Hintermüller, M.1    Ring, W.2
  • 15
    • 0000299558 scopus 로고    scopus 로고
    • Augmented Lagrangian methods for nonsmooth convex optimization in Hilbert spaces
    • Ito K., Kunisch K. Augmented Lagrangian methods for nonsmooth convex optimization in Hilbert spaces. Nonlinear Anal. TMA. 41:2000;573-589.
    • (2000) Nonlinear Anal. TMA , vol.41 , pp. 573-589
    • Ito, K.1    Kunisch, K.2
  • 16
    • 0037261943 scopus 로고    scopus 로고
    • Semi-smooth Newton methods for variational inequalities of the first kind
    • Ito K., Kunisch K. Semi-smooth Newton methods for variational inequalities of the first kind. Math. Modell. Numer. Anal. 37:2002;41-62.
    • (2002) Math. Modell. Numer. Anal. , vol.37 , pp. 41-62
    • Ito, K.1    Kunisch, K.2
  • 18
    • 0141672491 scopus 로고
    • Optimal Control for Parabolic Control Problems and Applications
    • Berlin: Springer
    • Tiba D. Optimal Control for Parabolic Control Problems and Applications. Lecture Notes in Mathematics. Vol. 1459:1990;Springer, Berlin.
    • (1990) Lecture Notes in Mathematics , vol.1459
    • Tiba, D.1
  • 19
    • 0000197665 scopus 로고    scopus 로고
    • Error estimates for the discretization of state constrained convex control problems
    • Tiba D., Tröltzsch F. Error estimates for the discretization of state constrained convex control problems. Numer. Funct. Anal. Optim. 17:1996;1005-1028.
    • (1996) Numer. Funct. Anal. Optim. , vol.17 , pp. 1005-1028
    • Tiba, D.1    Tröltzsch, F.2
  • 20
    • 0043244872 scopus 로고    scopus 로고
    • Semi-smooth Newton methods for operator equations in function spaces
    • Ulbrich M. Semi-smooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13:2002;805-842.
    • (2002) SIAM J. Optim. , vol.13 , pp. 805-842
    • Ulbrich, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.