메뉴 건너뛰기




Volumn 29, Issue 1, 2007, Pages 22-48

Numerical sensitivity analysis for the quantity of interest in PDE-constrained optimization

Author keywords

PDE constrained optimization; Quantity of interest; Sensitivity analysis

Indexed keywords

CONSTRAINED OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SENSITIVITY ANALYSIS;

EID: 39449098781     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050637273     Document Type: Article
Times cited : (17)

References (21)
  • 1
    • 0001167160 scopus 로고    scopus 로고
    • A finite element pressure gradient stabilization for the Stokes equations based on local projections
    • R. BECKER AND M. BRAACK, A finite element pressure gradient stabilization for the Stokes equations based on local projections, Calcolo, 38 (2001), pp. 173-199.
    • (2001) Calcolo , vol.38 , pp. 173-199
    • BECKER, R.1    BRAACK, M.2
  • 3
    • 33947237419 scopus 로고    scopus 로고
    • Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations
    • R. BECKER AND B. VEXLER, Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations, J. Comput. Phys., 206 (2005), pp. 95-110.
    • (2005) J. Comput. Phys , vol.206 , pp. 95-110
    • BECKER, R.1    VEXLER, B.2
  • 4
    • 0032635368 scopus 로고    scopus 로고
    • Primal-dual strategy for constrained optimal control problems
    • M. BERGOUNIOUX, K. ITO, AND K. KUNISCH, Primal-dual strategy for constrained optimal control problems, SIAM J. Control Optim., 37 (1999), pp. 1176-1194.
    • (1999) SIAM J. Control Optim , vol.37 , pp. 1176-1194
    • BERGOUNIOUX, M.1    ITO, K.2    KUNISCH, K.3
  • 6
    • 0002449719 scopus 로고
    • Implicit function theorems for generalized equations
    • A. DONTCHEV, Implicit function theorems for generalized equations, Math. Programming, 70 (1995), pp. 91-106.
    • (1995) Math. Programming , vol.70 , pp. 91-106
    • DONTCHEV, A.1
  • 7
    • 2342466141 scopus 로고    scopus 로고
    • Parametric sensitivity analysis in optimal control of a reaction-diffusion systempart I: Solution differentiability
    • R. GRIESSE, Parametric sensitivity analysis in optimal control of a reaction-diffusion systempart I: Solution differentiability, Numer. Funct. Anal. Optim., 25 (2004), pp. 93-117.
    • (2004) Numer. Funct. Anal. Optim , vol.25 , pp. 93-117
    • GRIESSE, R.1
  • 8
    • 1842764942 scopus 로고    scopus 로고
    • Parametric sensitivity analysis in optimal control of a reaction-diffusion system- part II: Practical methods and examples
    • R. GRIESSE, Parametric sensitivity analysis in optimal control of a reaction-diffusion system- part II: Practical methods and examples, Optim. Methods Softw., 19 (2004), pp. 217-242.
    • (2004) Optim. Methods Softw , vol.19 , pp. 217-242
    • GRIESSE, R.1
  • 9
    • 33644943921 scopus 로고    scopus 로고
    • A primal-dual active set strategy for optimal boundary control of a nonlinear reaction-diffusion system
    • R. GRIESSE AND S. VOLKWEIN, A primal-dual active set strategy for optimal boundary control of a nonlinear reaction-diffusion system, SIAM J. Control Optim., 44 (2005), pp. 467-494.
    • (2005) SIAM J. Control Optim , vol.44 , pp. 467-494
    • GRIESSE, R.1    VOLKWEIN, S.2
  • 10
    • 85160609827 scopus 로고    scopus 로고
    • R. GRIESSE AND S. VOLKWEIN, Parametric sensitivity analysis for optimal boundary control of a 3D reaction-diffusion system, in Large-Scale Nonlinear Optimization, G. D. Pillo and M. Roma, eds., Nonconvex Optim. Appl. 83, Springer-Verlag, New York, 2006, pp. 127-149.
    • R. GRIESSE AND S. VOLKWEIN, Parametric sensitivity analysis for optimal boundary control of a 3D reaction-diffusion system, in Large-Scale Nonlinear Optimization, G. D. Pillo and M. Roma, eds., Nonconvex Optim. Appl. 83, Springer-Verlag, New York, 2006, pp. 127-149.
  • 11
    • 0029777695 scopus 로고    scopus 로고
    • Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations
    • J. HEYWOOD, R. RANNACHER, AND S. TUREK, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 325-352.
    • (1996) Internat. J. Numer. Methods Fluids , vol.22 , pp. 325-352
    • HEYWOOD, J.1    RANNACHER, R.2    TUREK, S.3
  • 12
    • 0041657515 scopus 로고    scopus 로고
    • The primal-dual active set strategy as a semis- mooth Newton method
    • M. HINTERMÜLLER, K. ITO, AND K. KUNISCH, The primal-dual active set strategy as a semis- mooth Newton method, SIAM J. Optim., 13 (2003), pp. 865-888.
    • (2003) SIAM J. Optim , vol.13 , pp. 865-888
    • HINTERMÜLLER, M.1    ITO, K.2    KUNISCH, K.3
  • 13
    • 0036294683 scopus 로고    scopus 로고
    • Second order methods for optimal control of time-dependent fluid flow
    • M. HINZE AND K. KUNISCH, Second order methods for optimal control of time-dependent fluid flow, SIAM J. Control Optim., 40 (2001), pp. 925-946.
    • (2001) SIAM J. Control Optim , vol.40 , pp. 925-946
    • HINZE, M.1    KUNISCH, K.2
  • 14
    • 0030304771 scopus 로고    scopus 로고
    • Augmented Lagrangian-SQP-methods in Hubert spaces and application to control in the coefficients problem
    • K. ITO AND K. KUNISCH, Augmented Lagrangian-SQP-methods in Hubert spaces and application to control in the coefficients problem, SIAM J. Optim., 6 (1996), pp. 96-125.
    • (1996) SIAM J. Optim , vol.6 , pp. 96-125
    • ITO, K.1    KUNISCH, K.2
  • 15
    • 11144229487 scopus 로고    scopus 로고
    • The primal-dual active set method for nonlinear optimal control problems with bilateral constraints
    • K. ITO AND K. KUNISCH, The primal-dual active set method for nonlinear optimal control problems with bilateral constraints, SIAM J. Control Optim., 43 (2004), pp. 357-376.
    • (2004) SIAM J. Control Optim , vol.43 , pp. 357-376
    • ITO, K.1    KUNISCH, K.2
  • 16
    • 0038811738 scopus 로고    scopus 로고
    • Primal-dual active set strategy for a general class of constrained optimal control problems
    • K. KUNISCH AND A. RÖSCH, Primal-dual active set strategy for a general class of constrained optimal control problems, SIAM J. Optim., 13 (2002), pp. 321-334.
    • (2002) SIAM J. Optim , vol.13 , pp. 321-334
    • KUNISCH, K.1    RÖSCH, A.2
  • 17
    • 0030304773 scopus 로고    scopus 로고
    • An infinite-dimensional convergence theory for reduced SQP methods in Hilbert space
    • F.-S. KUPFER, An infinite-dimensional convergence theory for reduced SQP methods in Hilbert space, SIAM J. Optim., 6 (1996), pp. 126-163.
    • (1996) SIAM J. Optim , vol.6 , pp. 126-163
    • KUPFER, F.-S.1
  • 18
    • 0037005085 scopus 로고    scopus 로고
    • Sensitivity analysis for parametric optimal control of semilinear parabolic equations
    • K. MALANOWSKI, Sensitivity analysis for parametric optimal control of semilinear parabolic equations, J. Convex Anal., 9 (2002), pp. 543-561.
    • (2002) J. Convex Anal , vol.9 , pp. 543-561
    • MALANOWSKI, K.1
  • 19
    • 0002958234 scopus 로고
    • First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems
    • H. MAURER AND J. ZOWE, First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math. Programming, 16 (1979), pp. 98-110.
    • (1979) Math. Programming , vol.16 , pp. 98-110
    • MAURER, H.1    ZOWE, J.2
  • 20
    • 33748925762 scopus 로고    scopus 로고
    • A priori error estimates for the finite element discretization of elliptic parameter identification problems with pointwise measurements
    • R. RANNACHER AND B. VEXLER, A priori error estimates for the finite element discretization of elliptic parameter identification problems with pointwise measurements, SIAM J. Control Optim., 44 (2005), pp. 1844-1863.
    • (2005) SIAM J. Control Optim , vol.44 , pp. 1844-1863
    • RANNACHER, R.1    VEXLER, B.2
  • 21
    • 0002733529 scopus 로고    scopus 로고
    • Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations
    • Dyn. Contin. Discrete Impuls. Syst
    • F. TRÖLTZSCH, Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 7 (2000), pp. 289-306.
    • (2000) Ser. A Math. Anal , vol.7 , pp. 289-306
    • TRÖLTZSCH, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.