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Volumn 47, Issue 3, 2009, Pages 1666-1683

Moreau-yosida regularization in state constrained elliptic control problems: Error estimates and parameter adjustment

Author keywords

Elliptic optimal control problem; Error estimates; Moreau Yosida based regularization; Pointwise state constraints

Indexed keywords

APPROXIMATION ERRORS; DISCRETIZATION; ELLIPTIC CONTROL PROBLEMS; ELLIPTIC OPTIMAL CONTROL PROBLEM; ERROR ESTIMATES; FINITE-ELEMENT DISCRETIZATION; MESH SIZE; MOREAU-YOSIDA REGULARIZATION; MOREAU-YOSIDA-BASED REGULARIZATION; NUMERICAL SOLUTION; OPTIMAL CONTROL PROBLEM; OPTIMAL SELECTION; POINTWISE STATE CONSTRAINTS; REGULARIZATION PARAMETERS; THEORETICAL RESULT;

EID: 65949114048     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/080718735     Document Type: Article
Times cited : (75)

References (14)
  • 1
    • 16244389389 scopus 로고
    • 2 estimates for the finite element method for the Dirichlet problem with singular data
    • 2 estimates for the finite element method for the Dirichlet problem with singular data, Numer. Math., 47 (1985), pp. 627-632.
    • (1985) Numer. Math , vol.47 , pp. 627-632
    • CASAS, E.1
  • 3
    • 0022810709 scopus 로고
    • Control of an elliptic problem with pointwise state constraints
    • E. CASAS, Control of an elliptic problem with pointwise state constraints, SIAM J. Control Optim., 24 (1986), pp. 1309-1318.
    • (1986) SIAM J. Control Optim , vol.24 , pp. 1309-1318
    • CASAS, E.1
  • 4
    • 0000632437 scopus 로고
    • 2- projection into finite element function spaces
    • 2- projection into finite element function spaces, Numer. Math., 23 (1975), pp. 193-197.
    • (1975) Numer. Math , vol.23 , pp. 193-197
    • DOUGLAS, J.1    DUPONT, T.2    WAHLBIN, L.3
  • 5
    • 48449089214 scopus 로고    scopus 로고
    • Convergence of a finite element approximation to a stateconstrained elliptic control problem
    • K. DECKELNICK AND M. HINZE, Convergence of a finite element approximation to a stateconstrained elliptic control problem, SIAM J. Numer. Anal., 45 (2007), pp. 1937-1953.
    • (2007) SIAM J. Numer. Anal , vol.45 , pp. 1937-1953
    • DECKELNICK, K.1    HINZE, M.2
  • 6
    • 65949123937 scopus 로고    scopus 로고
    • K. DECKELNICK AND M. HINZE, A Finite Element Approximation to Elliptic Control Problems in the Presence of Control and State Constraints, Preprint HBAM2007-01, Hamburger Beiträge zur Angewandten Mathematik, Universität Hamburg, Hamburg, Germany, 2007.
    • K. DECKELNICK AND M. HINZE, A Finite Element Approximation to Elliptic Control Problems in the Presence of Control and State Constraints, Preprint HBAM2007-01, Hamburger Beiträge zur Angewandten Mathematik, Universität Hamburg, Hamburg, Germany, 2007.
  • 7
    • 65949116942 scopus 로고    scopus 로고
    • Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations
    • Springer, Berlin
    • K. DECKELNICK AND M. HINZE, Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations, Proceedings of ENUMATH 2007, Numerical Mathematics and Advanced Applications, Springer, Berlin, 2008, pp. 597-604.
    • (2008) Proceedings of ENUMATH 2007, Numerical Mathematics and Advanced Applications , pp. 597-604
    • DECKELNICK, K.1    HINZE, M.2
  • 8
    • 33847157898 scopus 로고    scopus 로고
    • Path-following methods for a class of constrained minimization problems in function space
    • M. HINTERMÜLLER AND K. KUNISCH, Path-following methods for a class of constrained minimization problems in function space, SIAM J. Optim., 17 (2006), pp. 159-187.
    • (2006) SIAM J. Optim , vol.17 , pp. 159-187
    • HINTERMÜLLER, M.1    KUNISCH, K.2
  • 9
    • 34547222933 scopus 로고    scopus 로고
    • Feasible and noninterior path-following in constrained minimization with low multiplier regularity
    • M. HINTERMÜLLER AND K. KUNISCH, Feasible and noninterior path-following in constrained minimization with low multiplier regularity, SIAM J. Control Optim., 45 (2006), pp. 1198-1221.
    • (2006) SIAM J. Control Optim , vol.45 , pp. 1198-1221
    • HINTERMÜLLER, M.1    KUNISCH, K.2
  • 10
    • 65949102450 scopus 로고    scopus 로고
    • Mesh-independence and fast local convergence of a primal-dual activeset method for mixed control-state constrained elliptic problems
    • M. HINTERMÜLLER, Mesh-independence and fast local convergence of a primal-dual activeset method for mixed control-state constrained elliptic problems, ANZIAM J., 49 (2007), pp. 1-38.
    • (2007) ANZIAM J , vol.49 , pp. 1-38
    • HINTERMÜLLER, M.1
  • 11
    • 14844350073 scopus 로고    scopus 로고
    • A variational discretization concept in control constrained optimization: The linearquadratic case
    • M. HINZE, A variational discretization concept in control constrained optimization: The linearquadratic case, Comput. Optim. Appl., 30 (2005), pp. 45-61.
    • (2005) Comput. Optim. Appl , vol.30 , pp. 45-61
    • HINZE, M.1
  • 12
    • 77954953886 scopus 로고    scopus 로고
    • Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems
    • M. HINZE AND C. MEYER, Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems, Comput. Optim. Appl., 1 (2008).
    • (2008) Comput. Optim. Appl , vol.1
    • HINZE, M.1    MEYER, C.2
  • 13
    • 65949107233 scopus 로고    scopus 로고
    • M. HINZE AND A. SCHIELA, Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment, Preprint SPP1253-08-03, German Research Foundation, Priority Programme 1253, Universit ät Erlangen, 2007.
    • M. HINZE AND A. SCHIELA, Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment, Preprint SPP1253-08-03, German Research Foundation, Priority Programme 1253, Universit ät Erlangen, 2007.
  • 14
    • 84966250424 scopus 로고
    • ∞ estimates for the finite element method on irregular meshes
    • ∞ estimates for the finite element method on irregular meshes, Math. Comp., 30 (1976), pp. 681-897.
    • (1976) Math. Comp , vol.30 , pp. 681-897
    • SCOTT, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.