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Volumn 117, Issue 1-2, 2009, Pages 435-485

Primal-dual interior-point methods for PDE-constrained optimization

Author keywords

Control constraints; Global convergence; Optimal control; PDE constraints; Primal dual interior point methods; Superlinear convergence

Indexed keywords

AIRCRAFT ENGINES; CONSTRAINT THEORY; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 46749103269     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0168-7     Document Type: Article
Times cited : (40)

References (27)
  • 1
    • 0022661397 scopus 로고
    • A mesh-independence principle for operator equations and their disetizations
    • Allgower E., Böhmer K., Potra F., Rheinboldt W. (1986). A mesh-independence principle for operator equations and their disetizations. SIAM J. Numer. Anal. 23: 160-169
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 160-169
    • Allgower, E.1    Böhmer, K.2    Potra, F.3    Rheinboldt, W.4
  • 3
    • 0034353740 scopus 로고    scopus 로고
    • A comparison of a moreau-yosida based active set strategy and interior point methods for constrained optimal control problems
    • Bergounioux M., Haddou M., Hintermüller M., Kunisch K. (2000). A comparison of a moreau-yosida based active set strategy and interior point methods for constrained optimal control problems. SIAM J. Optim. 11: 495-521
    • (2000) SIAM J. Optim. , vol.11 , pp. 495-521
    • Bergounioux, M.1    Haddou, M.2    Hintermüller, M.3    Kunisch, K.4
  • 4
    • 0032635368 scopus 로고    scopus 로고
    • Primal-dual strategy for constrained optimal control problems
    • 4
    • Bergounioux M., Ito K., Kunisch K. (1999). Primal-dual strategy for constrained optimal control problems. SIAM J. Control Optim. 37(4): 1176-1194
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1176-1194
    • Bergounioux, M.1    Ito, K.2    Kunisch, K.3
  • 5
    • 0032096712 scopus 로고    scopus 로고
    • Optimization problems with perturbations: A guided tour
    • 2
    • Bonnans J.F., Shapiro A. (1998). Optimization problems with perturbations: a guided tour. SIAM Rev. 40(2): 228-264
    • (1998) SIAM Rev. , vol.40 , pp. 228-264
    • Bonnans, J.F.1    Shapiro, A.2
  • 6
    • 0036959271 scopus 로고    scopus 로고
    • Interior methods for nonlinear optimization
    • Forsgren A., Gill P.E., Wright M.H. (2002). Interior methods for nonlinear optimization. SIAM Rev. 44: 525-597
    • (2002) SIAM Rev. , vol.44 , pp. 525-597
    • Forsgren, A.1    Gill, P.E.2    Wright, M.H.3
  • 7
    • 0041657515 scopus 로고    scopus 로고
    • The primal-dual active set strategy as a semismooth Newton method
    • 3
    • Hintermüller M., Ito K., Kunisch K. (2003). The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13(3): 865-888
    • (2003) SIAM J. Optim. , vol.13 , pp. 865-888
    • Hintermüller, M.1    Ito, K.2    Kunisch, K.3
  • 8
    • 23944469842 scopus 로고    scopus 로고
    • A mesh-independence result for semismooth Newton methods
    • 1
    • Hintermüller M., Ulbrich M. (2004). A mesh-independence result for semismooth Newton methods. Math. Program. Ser. B 101(1): 151-184
    • (2004) Math. Program. Ser. B , vol.101 , pp. 151-184
    • Hintermüller, M.1    Ulbrich, M.2
  • 9
    • 0036294683 scopus 로고    scopus 로고
    • Second order methods for optimal control of time-dependent fluid flow
    • electronic
    • Hinze, M., Kunisch, K.: Second order methods for optimal control of time-dependent fluid flow. SIAM J. Control Optim. 40(3), 925-946 (electronic) (2001)
    • (2001) SIAM J. Control Optim. , vol.40 , Issue.3 , pp. 925-946
    • Hinze, M.1    Kunisch, K.2
  • 11
    • 0001741739 scopus 로고
    • Multilevel algorithms for constrained compact fixed point problems
    • Kelley C.T., Sachs E.W. (1994). Multilevel algorithms for constrained compact fixed point problems. SIAM J. Sci. Comput. 15: 645-667
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 645-667
    • Kelley, C.T.1    Sachs, E.W.2
  • 12
    • 0034255203 scopus 로고    scopus 로고
    • Solving elliptic control problems with interior point and SQP methods: Control and state constraints
    • Mittelmann H.D., Maurer H. (2000). Solving elliptic control problems with interior point and SQP methods: Control and state constraints. J. Comp. Appl. Math. 120: 175-195
    • (2000) J. Comp. Appl. Math. , vol.120 , pp. 175-195
    • Mittelmann, H.D.1    Maurer, H.2
  • 13
    • 46749092254 scopus 로고    scopus 로고
    • The convergence of an interior point method for an elliptic control problem with mixed control-state constraints
    • to appear
    • Prüfert, U., Tröltzsch, F., Weiser, M.: The convergence of an interior point method for an elliptic control problem with mixed control-state constraints. Comp. Opt. Appl. (to appear)
    • Comp. Opt. Appl.
    • Prüfert, U.1    Tröltzsch, F.2    Weiser, M.3
  • 14
    • 22344452761 scopus 로고    scopus 로고
    • A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations
    • 7
    • Kunisch K., los Reyes J.C. (2005). A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations. Nonlinear Anal. 62(7): 1289-1316
    • (2005) Nonlinear Anal. , vol.62 , pp. 1289-1316
    • De Los Reyes, J.C.1    Kunisch, K.2
  • 15
    • 0016993914 scopus 로고
    • Stability theory for systems of inequalities. II: Differentiable nonlinear systems
    • Robinson S.M. (1976). Stability theory for systems of inequalities. II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13: 497-513
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 497-513
    • Robinson, S.M.1
  • 16
    • 46749086004 scopus 로고    scopus 로고
    • Superlinear convergence of the control reduced interior point method for PDE constrained optimization
    • to appear
    • Schiela, A., Weiser, M.: Superlinear convergence of the control reduced interior point method for PDE constrained optimization. Comp. Opt. Appl. (to appear)
    • Comp. Opt. Appl.
    • Schiela, A.1    Weiser, M.2
  • 19
    • 0037445067 scopus 로고    scopus 로고
    • Constrained optimal control of Navier-Stokes flow by semismooth Newton methods
    • 3-4
    • Ulbrich M. (2003). Constrained optimal control of Navier-Stokes flow by semismooth Newton methods. Syst. Control Lett. 48(3-4): 297-311
    • (2003) Syst. Control Lett. , vol.48 , pp. 297-311
    • Ulbrich, M.1
  • 20
    • 0043244872 scopus 로고    scopus 로고
    • Semismooth Newton methods for operator equations in function spaces
    • 3
    • Ulbrich M. (2003). Semismooth Newton methods for operator equations in function spaces. SIAM J.Optim. 13(3): 805-841
    • (2003) SIAM J.Optim. , vol.13 , pp. 805-841
    • Ulbrich, M.1
  • 21
    • 0032651455 scopus 로고    scopus 로고
    • Global convergence of trust-region interior-point algorithms for infinite-dimensional nonconvex minimization subject to pointwise bounds
    • 3
    • Ulbrich M., Ulbrich S. (1999). Global convergence of trust-region interior-point algorithms for infinite-dimensional nonconvex minimization subject to pointwise bounds. SIAM J. Control Optim. 37(3): 731-764
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 731-764
    • Ulbrich, M.1    Ulbrich, S.2
  • 22
    • 0034544017 scopus 로고    scopus 로고
    • Superlinear convergence of affine-scaling interior-point Newton methods for infinite-dimensional nonlinear problems with pointwise bounds
    • 6
    • Ulbrich M., Ulbrich S. (2000). Superlinear convergence of affine-scaling interior-point Newton methods for infinite-dimensional nonlinear problems with pointwise bounds. SIAM J. Control Optim. 38(6): 1938-1984
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 1938-1984
    • Ulbrich, M.1    Ulbrich, S.2
  • 23
    • 33748918597 scopus 로고    scopus 로고
    • Interior point methods in function space
    • 5
    • Weiser M. (2005). Interior point methods in function space. SIAM J. Control Optim. 44(5): 1766-1786
    • (2005) SIAM J. Control Optim. , vol.44 , pp. 1766-1786
    • Weiser, M.1
  • 24
    • 44649087708 scopus 로고    scopus 로고
    • Inexact central path following algorithms for optimal control problems
    • to appear
    • Weiser, M., Deuflhard, P.: Inexact central path following algorithms for optimal control problems. SIAM J. Control Optim. (to appear)
    • SIAM J. Control Optim.
    • Weiser, M.1    Deuflhard, P.2
  • 25
    • 46749096492 scopus 로고    scopus 로고
    • A control reduced primal interior point method for a class of control constrained optimal control problems
    • to appear
    • Weiser, M., Gänzler, T., Schiela, A.: A control reduced primal interior point method for a class of control constrained optimal control problems. Comp. Opt. Appl. (to appear)
    • Comp. Opt. Appl.
    • Weiser, M.1    Gänzler, T.2    Schiela, A.3
  • 26
    • 38949124443 scopus 로고    scopus 로고
    • Function space interior point methods for PDE constrained optimization
    • 1
    • Weiser M., Schiela A. (2004). Function space interior point methods for PDE constrained optimization. PAMM 4(1): 43-46
    • (2004) PAMM , vol.4 , pp. 43-46
    • Weiser, M.1    Schiela, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.