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Volumn 9, Issue 4, 1999, Pages 1064-1081

A trust region method for parabolic boundary control problems

Author keywords

Inexact Newton methods; Optimal control; Trust region methods

Indexed keywords


EID: 0033448149     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623496308965     Document Type: Article
Times cited : (19)

References (23)
  • 1
    • 84966275544 scopus 로고
    • Minimization of functions having Lipschitz-continuous first partial derivatives
    • L. ARMIJO, Minimization of functions having Lipschitz-continuous first partial derivatives, Pacific J. Math., 16 (1966), pp. 1-3.
    • (1966) Pacific J. Math. , vol.16 , pp. 1-3
    • Armijo, L.1
  • 2
    • 0016948909 scopus 로고
    • On the Goldstein-Levitin-Polyak gradient projection method
    • D. P. BERTSEKAS, On the Goldstein-Levitin-Polyak gradient projection method, IEEE Trans. Automat. Control, 21 (1976), pp. 174-184.
    • (1976) IEEE Trans. Automat. Control , vol.21 , pp. 174-184
    • Bertsekas, D.P.1
  • 3
    • 0000377218 scopus 로고
    • Projected Newton methods for optimization problems with simple constraints
    • D. P. BERTSEKAS, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim., 20 (1982), pp. 221-246.
    • (1982) SIAM J. Control Optim. , vol.20 , pp. 221-246
    • Bertsekas, D.P.1
  • 4
    • 0004003433 scopus 로고
    • Numerical solution of initial-value problems in differential-algebraic equations
    • SIAM, Philadelphia
    • K. E. BRENAN, S. L. CAMPBELL, AND L. R. PETZOLD, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Classics Appl. Math. 14, SIAM, Philadelphia, 1995.
    • (1995) Classics Appl. Math. , vol.14
    • Brenan, K.E.1    Campbell, S.L.2    Petzold, L.R.3
  • 5
    • 0000286812 scopus 로고
    • Using Krylov methods in the solution of large-scale differential-algebraic systems
    • P. N. BROWN, A. C. HINDMARSH, AND L. R. PETZOLD, Using Krylov methods in the solution of large-scale differential-algebraic systems, SIAM J. Sci. Comput., 15 (1994), pp. 1467-1488.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1467-1488
    • Brown, P.N.1    Hindmarsh, A.C.2    Petzold, L.R.3
  • 6
    • 0000615467 scopus 로고    scopus 로고
    • Consistent initial condition calculation for differential-algebraic systems
    • P. N. BROWN, A. C. HINDMARSH, AND L. R. PETZOLD, Consistent initial condition calculation for differential-algebraic systems, SIAM J. Sci. Comput., 19 (1998), pp. 1495-1512.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1495-1512
    • Brown, P.N.1    Hindmarsh, A.C.2    Petzold, L.R.3
  • 7
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization problems with simple bounds
    • A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, Global convergence of a class of trust region algorithms for optimization problems with simple bounds, SIAM J. Numer. Anal., 25 (1988), pp. 433-460.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 8
    • 84966215545 scopus 로고
    • Testing a class of methods for solving minimization problems with simple bounds on the variables
    • A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, Testing a class of methods for solving minimization problems with simple bounds on the variables, Math. Comp., 50 (1988), pp. 399-430.
    • (1988) Math. Comp. , vol.50 , pp. 399-430
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 10
    • 0003315567 scopus 로고    scopus 로고
    • Numerical methods for unconstrained optimization and nonlinear equations
    • SIAM, Philadelphia
    • J. E. DENNIS, JR. AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics Appl. Math. 16, SIAM, Philadelphia, 1996.
    • (1996) Classics Appl. Math. , vol.16
    • Dennis J.E., Jr.1    Schnabel, R.B.2
  • 11
    • 0001995010 scopus 로고
    • Identification of the support of nonsmoothness
    • W. W. Hager, D. W. Hearn, and P. Pardalos, eds., Kluwer Academic Publishers B.V., Boston
    • C. T. KELLEY, Identification of the support of nonsmoothness, in Large Scale Optimization: State of the Art, W. W. Hager, D. W. Hearn, and P. Pardalos, eds., Kluwer Academic Publishers B.V., Boston, 1994, pp. 192-205.
    • (1994) Large Scale Optimization: State of the Art , pp. 192-205
    • Kelley, C.T.1
  • 12
    • 0002914778 scopus 로고
    • Iterative methods for linear and nonlinear equations
    • SIAM, Philadelphia
    • C. T. KELLEY, Iterative Methods for Linear and Nonlinear Equations, Frontiers Appl. Math. 16, SIAM, Philadelphia, 1995.
    • (1995) Frontiers Appl. Math. , vol.16
    • Kelley, C.T.1
  • 13
    • 0012767374 scopus 로고
    • Fast algorithms for compact fixed point problems with inexact function evaluations
    • C. T. KELLEY AND E. W. SACHS, Fast algorithms for compact fixed point problems with inexact function evaluations, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 725-742.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 725-742
    • Kelley, C.T.1    Sachs, E.W.2
  • 14
    • 0001741739 scopus 로고
    • Multilevel algorithms for constrained compact fixed point problems
    • C. T. KELLEY AND E. W. SACHS, Multilevel algorithms for constrained compact fixed point problems, SIAM J. Sci. Comput., 15 (1994), pp. 645-667.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 645-667
    • Kelley, C.T.1    Sachs, E.W.2
  • 15
    • 0022145863 scopus 로고
    • Projected Hessian updating algorithms for nonlinearly constrained optimization
    • J. NOCEDAL AND M. L. OVERTON, Projected Hessian updating algorithms for nonlinearly constrained optimization, SIAM J. Numer. Anal., 22 (1985), pp. 821-850.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 821-850
    • Nocedal, J.1    Overton, M.L.2
  • 16
    • 0002753571 scopus 로고
    • A description of DASSL: A differential/algebraic system solver
    • R. S. Stepleman et al., eds., North-Holland, Amsterdam, The Netherlands
    • L. R. PETZOLD, A description of DASSL: A differential/algebraic system solver, in Scientific Computing, R. S. Stepleman et al., eds., North-Holland, Amsterdam, The Netherlands, 1983, pp. 65-68.
    • (1983) Scientific Computing , pp. 65-68
    • Petzold, L.R.1
  • 17
    • 0002302301 scopus 로고
    • Convergence properties of a class of minimization algorithms
    • O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York
    • M. J. D. POWELL, Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1975, pp. 1-27.
    • (1975) Nonlinear Programming , vol.2 , pp. 1-27
    • Powell, M.J.D.1
  • 18
    • 0018020468 scopus 로고
    • A parabolic control problem with a boundary condition of the Stefan-Boltzmann type
    • E. SACHS, A parabolic control problem with a boundary condition of the Stefan-Boltzmann type, Z. Angew. Math. Mech., 58 (1978), pp. 443-449.
    • (1978) Z. Angew. Math. Mech. , vol.58 , pp. 443-449
    • Sachs, E.1
  • 19
    • 0000305846 scopus 로고
    • The conjugate gradient method and trust regions in large scale optimization
    • T. STEIHAUG, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626-637.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 626-637
    • Steihaug, T.1
  • 20
    • 0002633896 scopus 로고
    • Towards an efficient sparsity exploiting Newton method for minimization
    • I. S. Duff, ed., Academic Press, London
    • PH. L. TOINT, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57-88.
    • (1981) Sparse Matrices and Their Uses , pp. 57-88
    • Toint, Ph.L.1
  • 21
    • 0000198907 scopus 로고
    • Global convergence of a class of trust-region methods for nonconvex minimization in Hilbert space
    • PH. L. TOINT, Global convergence of a class of trust-region methods for nonconvex minimization in Hilbert space, IMA J. Numer. Anal., 8 (1988), pp. 231-252.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 231-252
    • Toint, Ph.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.