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Volumn 19, Issue 3, 2000, Pages 214-224

Interior point multigrid methods for topology optimization

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; TOPOLOGY;

EID: 0034186238     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001580050104     Document Type: Article
Times cited : (42)

References (39)
  • 2
    • 0000719421 scopus 로고
    • A new method for optimal truss topology design
    • Ben-Tal, A.; Bendsøe, M. 1993: A new method for optimal truss topology design. SIAM J. Optimiz. 3, 322-358
    • (1993) SIAM J. Optimiz. , vol.3 , pp. 322-358
    • Ben-Tal, A.1    Bendsøe, M.2
  • 3
    • 0000704645 scopus 로고
    • Potential reduction polynomial time method for truss topology design
    • Ben-Tal, A.; Nemirovskii, A. 1994: Potential reduction polynomial time method for truss topology design. SIAM J. Optimiz. 4, 596-612
    • (1994) SIAM J. Optimiz. , vol.4 , pp. 596-612
    • Ben-Tal, A.1    Nemirovskii, A.2
  • 5
    • 0024105011 scopus 로고
    • Generating optimal topologies in structural design using a homogenization method
    • Bendsøe, M.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method. Comp. Meth. Appl. Mech. Eng. 71, 197-224
    • (1988) Comp. Meth. Appl. Mech. Eng. , vol.71 , pp. 197-224
    • Bendsøe, M.1    Kikuchi, N.2
  • 6
    • 84966214346 scopus 로고
    • A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems
    • Bramble, J.; Pasciak, J. 1988: A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Math. Comp. 50, 1-17
    • (1988) Math. Comp. , vol.50 , pp. 1-17
    • Bramble, J.1    Pasciak, J.2
  • 7
    • 0003689529 scopus 로고    scopus 로고
    • A trust region method based on interior point techniques for nonlinear programming
    • Argonne National Laboratory, Argonne, ILL
    • Byrd, R.; Gilbert, J.; Nocedal, J. 1996: A trust region method based on interior point techniques for nonlinear programming. Technical Report OTC 96/02, Argonne National Laboratory, Argonne, ILL
    • (1996) Technical Report OTC 96/02
    • Byrd, R.1    Gilbert, J.2    Nocedal, J.3
  • 8
    • 0004212720 scopus 로고    scopus 로고
    • An interior point algorithm for large-scale nonlinear programming
    • Northwestern University, Evanston, ILL
    • Byrd, R.; Hribar, M.; Nocedal, J. 1997: An interior point algorithm for large-scale nonlinear programming. Technical Report, Northwestern University, Evanston, ILL
    • (1997) Technical Report
    • Byrd, R.1    Hribar, M.2    Nocedal, J.3
  • 9
    • 0012691880 scopus 로고    scopus 로고
    • On the local behavior of an interior point method for nonlinear programming
    • Argonne National Laboratory, Argonne, ILL
    • Byrd, R.; Liu, G.; Nocedal, J. 1998: On the local behavior of an interior point method for nonlinear programming. Technical Report OTC 98/02, Argonne National Laboratory, Argonne, ILL
    • (1998) Technical Report OTC 98/02
    • Byrd, R.1    Liu, G.2    Nocedal, J.3
  • 10
    • 0039070620 scopus 로고    scopus 로고
    • A primal-dual algorithm for minimizing a nonconvex function subject to bound and linear equality constraints
    • IBM T.J. Watson Research Center, Yorktown Heights, NY
    • Conn, A.; Gould, N.; Toint, P. 1996: A primal-dual algorithm for minimizing a nonconvex function subject to bound and linear equality constraints. Technical Report RC 20639, IBM T.J. Watson Research Center, Yorktown Heights, NY
    • (1996) Technical Report RC 20639
    • Conn, A.1    Gould, N.2    Toint, P.3
  • 11
    • 84966216063 scopus 로고
    • The numerical solution of equality-constrained quadratic programming problems
    • Dyn, N.; Ferguson, W. 1983: The numerical solution of equality-constrained quadratic programming problems. Math. Comp. 41, 165-170
    • (1983) Math. Comp. , vol.41 , pp. 165-170
    • Dyn, N.1    Ferguson, W.2
  • 12
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of the Newton interior-point method for nonlinear programming
    • El-Bakry, A.; Tapia, R.; Tsuchiya, T.; Zhang, Y. 1996: On the formulation and theory of the Newton interior-point method for nonlinear programming. J. Optimiz. Theory Appl. 89, 507-541
    • (1996) J. Optimiz. Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.1    Tapia, R.2    Tsuchiya, T.3    Zhang, Y.4
  • 14
    • 0003459687 scopus 로고    scopus 로고
    • A primal-dual interior method for nonconvex nonlinear programming
    • Computing Sciences Research Center, Bell Laboratories, Murray Hill, NJ
    • Gay, D.; Overton, M.; Wright, M. 1997: A primal-dual interior method for nonconvex nonlinear programming. Technical Report 97-4-08, Computing Sciences Research Center, Bell Laboratories, Murray Hill, NJ
    • (1997) Technical Report 97-4-08
    • Gay, D.1    Overton, M.2    Wright, M.3
  • 16
    • 0019050749 scopus 로고
    • Fast solution of elliptic control problems
    • Hackbusch, W. 1980: Fast solution of elliptic control problems. J. Optimiz. Theory Appl. 31, 565-581
    • (1980) J. Optimiz. Theory Appl. , vol.31 , pp. 565-581
    • Hackbusch, W.1
  • 18
    • 6744249368 scopus 로고
    • The numerical solution of a control problem governed by a phase field model
    • Virginia Polytechnic Institute and State University
    • Heinkenschloss, M. 1995: The numerical solution of a control problem governed by a phase field model. Technical Report ICAM Report 95-12-01, Virginia Polytechnic Institute and State University
    • (1995) Technical Report ICAM Report 95-12-01
    • Heinkenschloss, M.1
  • 19
    • 0039165708 scopus 로고    scopus 로고
    • Optimal truss design by interior-point methods
    • Jarre, F.; Kočvara, M.; Zowe, J. 1998: Optimal truss design by interior-point methods. SIAM J. Optimiz. 8, 1084-1107
    • (1998) SIAM J. Optimiz. , vol.8 , pp. 1084-1107
    • Jarre, F.1    Kočvara, M.2    Zowe, J.3
  • 20
    • 0028433884 scopus 로고
    • Extended exact solutions for least-weight truss layouts, Part ii, unsymmetric cantilevers
    • Lewinski, T.; Zhou, M.; Rozvany, G.I.N. 1994: Extended exact solutions for least-weight truss layouts, Part ii, unsymmetric cantilevers. Int. J. Mech. Sci. 36, 399-414
    • (1994) Int. J. Mech. Sci. , vol.36 , pp. 399-414
    • Lewinski, T.1    Zhou, M.2    Rozvany, G.I.N.3
  • 22
    • 0003123391 scopus 로고
    • Some explorations in the genesis of structures
    • Bendsøe, M.; Soares, C. M. (eds.) Dordrecht: Kluwer
    • Mlejnek, H. 1993: Some explorations in the genesis of structures. In Bendsøe, M.; Soares, C. M. (eds.) Topology Design of Structures, pp. 287-300. Dordrecht: Kluwer
    • (1993) Topology Design of Structures , pp. 287-300
    • Mlejnek, H.1
  • 24
    • 21344467884 scopus 로고    scopus 로고
    • Numerical optimization of the cross-sectional shape of turbine blades
    • Schulz, V. 1996: Numerical optimization of the cross-sectional shape of turbine blades. Zeitschrift für angewandte Mathematik und Mechanik 76(S1), 207-210
    • (1996) Zeitschrift für Angewandte Mathematik und Mechanik , vol.76 , Issue.S1 , pp. 207-210
    • Schulz, V.1
  • 25
    • 84904997650 scopus 로고    scopus 로고
    • Solving discretized optimization problems by partially reduced SQP methods
    • Schulz, V. 1998: Solving discretized optimization problems by partially reduced SQP methods. Computing Visualization Sci. 12, 83-96
    • (1998) Computing Visualization Sci. , vol.12 , pp. 83-96
    • Schulz, V.1
  • 27
    • 6744226829 scopus 로고    scopus 로고
    • Special issue on SQP-based direct discretization methods for practical optimal control problems
    • to appear
    • Schulz, V. (guest-editor) 1999: Special issue on SQP-based direct discretization methods for practical optimal control problems. J. Comp. Appl. Math, (to appear)
    • (1999) J. Comp. Appl. Math
    • Schulz, V.1
  • 28
    • 0032860632 scopus 로고    scopus 로고
    • Conditional statistical inverse modeling in ground-water flow by multigrid methods
    • to appear
    • Schulz, V.; Bardossy, A.; Helmig, R. 1999: Conditional statistical inverse modeling in ground-water flow by multigrid methods. Computational Geosci. (to appear)
    • (1999) Computational Geosci.
    • Schulz, V.1    Bardossy, A.2    Helmig, R.3
  • 29
    • 0008418442 scopus 로고    scopus 로고
    • Optimum shape design of turbine blades
    • Kleinschmidt, P.; Bachem, A.; Derigs, U.; Fischer, D.: Leopold-Wildburger, U.; Möhring, R. (eds.) Berlin, Heidelberg, New York: Springer
    • Schulz, V.; Dreyer, T.; Speer, T.; Bock, H. 1996: Optimum shape design of turbine blades. In: Kleinschmidt, P.; Bachem, A.; Derigs, U.; Fischer, D.: Leopold-Wildburger, U.; Möhring, R. (eds.) Operations Research Proc. 1995, pp. 190-195. Berlin, Heidelberg, New York: Springer
    • (1996) Operations Research Proc. 1995 , pp. 190-195
    • Schulz, V.1    Dreyer, T.2    Speer, T.3    Bock, H.4
  • 30
    • 0008503537 scopus 로고    scopus 로고
    • Multigrid optimization methods for stationary parameter identification problems in groundwater flow
    • Hackbusch, W.; Wittum, G. (eds.) Berlin, Heidelberg, New York: Springer
    • Schulz, V.; Wittum, G. 1998: Multigrid optimization methods for stationary parameter identification problems in groundwater flow. In: Hackbusch, W.; Wittum, G. (eds.) Multigrid methods V, Lecture notes in computational science and engineering 3, pp. 276-288 Berlin, Heidelberg, New York: Springer
    • (1998) Multigrid Methods V, Lecture Notes in Computational Science and Engineering 3 , pp. 276-288
    • Schulz, V.1    Wittum, G.2
  • 31
    • 6744230249 scopus 로고    scopus 로고
    • Transforming smoothers for optimization saddlepoint problems
    • submitted
    • Schulz, V.; Wittum, G. 1999: Transforming smoothers for optimization saddlepoint problems. Computing (submitted)
    • (1999) Computing
    • Schulz, V.1    Wittum, G.2
  • 32
    • 0032137868 scopus 로고    scopus 로고
    • Numerical instabilities in topology optimization, a survey on procedures dealing with checkerboards, mesh-dependencies and local minima
    • Sigmund, O.; Petersson, J. 1998: Numerical instabilities in topology optimization, A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Optim. 16, 68-75
    • (1998) Struct. Optim. , vol.16 , pp. 68-75
    • Sigmund, O.1    Petersson, J.2
  • 33
    • 0023287947 scopus 로고
    • The method of moving asymptotes - A new method for structural optimization
    • Svanberg, K. 1987: The method of moving asymptotes - a new method for structural optimization. Int. J. Num. Meth. Eng. 24, 359-373
    • (1987) Int. J. Num. Meth. Eng. , vol.24 , pp. 359-373
    • Svanberg, K.1
  • 35
    • 0004212718 scopus 로고    scopus 로고
    • An interior point algorithm for nonconvex nonlinear programming
    • Statistics and Operations Research, Princeton University
    • Vanderbei, R.; Shanno, D. 1997: An interior point algorithm for nonconvex nonlinear programming. Technical Report SOR-97-21, Statistics and Operations Research, Princeton University
    • (1997) Technical Report SOR-97-21
    • Vanderbei, R.1    Shanno, D.2
  • 36
    • 0001584397 scopus 로고
    • Multi-grid methods for the Stokes and Navier-Stokes equations
    • Wittum, G. 1989a: Multi-grid methods for the Stokes and Navier-Stokes equations. Numerische Mathematik 54, 543-563
    • (1989) Numerische Mathematik , vol.54 , pp. 543-563
    • Wittum, G.1
  • 37
    • 0002801220 scopus 로고
    • On the convergence of multigrid methods with transforming smoothers, theory with application to the Navier-Stokes equations
    • Wittum, G. 1989b: On the convergence of multigrid methods with transforming smoothers, theory with application to the Navier-Stokes equations. Numerische Mathematik 57, 15-38
    • (1989) Numerische Mathematik , vol.57 , pp. 15-38
    • Wittum, G.1
  • 38
    • 0001444320 scopus 로고
    • A globally convergent version of the method of moving asymptotes
    • Zillober, C. 1993: A globally convergent version of the method of moving asymptotes. Struct. Optim. 6, 166-174
    • (1993) Struct. Optim. , vol.6 , pp. 166-174
    • Zillober, C.1


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