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Volumn 3, Issue 1, 2003, Pages 159-176

Applications of primal-dual interior methods in structural optimization

Author keywords

eddy current equations; elasticity equations; nonlinear programming; primal dual interiorpoint methods; structural optimization

Indexed keywords


EID: 33745319933     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2003-0011     Document Type: Article
Times cited : (5)

References (28)
  • 2
    • 0034353740 scopus 로고    scopus 로고
    • A comparison of a Moreau-Yosida based active set strategy and interior point methods for constrained optimal control problems
    • M. Bergounioux, M. Haddou, M. Hintermiiller, and K. Kunisch, A comparison of a Moreau-Yosida based active set strategy and interior point methods for constrained optimal control problems, SIAM J. Optim., 11 (2000), pp. 495-521.
    • (2000) SIAM J. Optim. , vol.11 , pp. 495-521
    • Bergounioux, M.1    Haddou, M.2    Hintermiiller, M.3    Kunisch, K.4
  • 3
    • 0029307478 scopus 로고
    • Various FEM formulations for the calculation of transient 3d eddy currents in nonlinear media
    • O. Biro and K. Preis, Various FEM formulations for the calculation of transient 3d eddy currents in nonlinear media, IEEE Transactions on Magnetics, 31 (1995), pp. 1307-1312.
    • (1995) IEEE Transactions on Magnetics , vol.31 , pp. 1307-1312
    • Biro, O.1    Preis, K.2
  • 4
    • 0001130234 scopus 로고    scopus 로고
    • A trust region method based on interior point techniques for nonlinear programming
    • R. H. Byrd, J. C. Gilbert, and J. Nocedal, A trust region method based on interior point techniques for nonlinear programming, Math. Program., Ser. A, 9 (2000), pp. 149-185.
    • (2000) Math. Program., Ser. A , vol.9 , pp. 149-185
    • Byrd, R.H.1    Gilbert, J.C.2    Nocedal, J.3
  • 6
    • 0002674910 scopus 로고
    • The watchdog technique for forcing convergence in algorithms for constrained optimization
    • R. M. Chamberlain, C. Lemarechal, H. C. Pedersen, and M. J. D. Powell, The watchdog technique for forcing convergence in algorithms for constrained optimization, Math. Program. Study, 16 (1982), pp. 117.
    • (1982) Math. Program. Study , vol.16
    • Chamberlain, R.M.1    Lemarechal, C.2    Pedersen, H.C.3    Powell, M.J.D.4
  • 7
    • 0000317378 scopus 로고    scopus 로고
    • A primal-dual trust-region algorithm for non-convex nonlinear programming
    • A. R. Conn, N. I. M. Gould, D. Orban, P. L. Toint, A primal-dual trust-region algorithm for non-convex nonlinear programming, Math. Program., Ser. B, 87 (2000), pp. 215-249.
    • (2000) Math. Program., Ser. B , vol.87 , pp. 215-249
    • Conn, A.R.1    Gould, N.I.M.2    Orban, D.3    Toint, P.L.4
  • 8
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of the Newton interior-point method for nonlinear programming
    • A. S. El-Bakry, R. A. Tapia, T. Tsuchiya, and Y. Zhang, On the formulation and theory of the Newton interior-point method for nonlinear programming, J. Optimization Theory Appl., 89 (1996), pp. 507-541.
    • (1996) J. Optimization Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.S.1    Tapia, R.A.2    Tsuchiya, T.3    Zhang, Y.4
  • 11
    • 0032358968 scopus 로고    scopus 로고
    • Primal-dual interior methods for nonconvex nonlinear programming
    • A. Forsgen and P. E. Gill, Primal-dual interior methods for nonconvex nonlinear programming, SIAM J. Optim., 8 (1998), pp. 1132-1152.
    • (1998) SIAM J. Optim. , vol.8 , pp. 1132-1152
    • Forsgen, A.1    Gill, P.E.2
  • 12
    • 0030531116 scopus 로고    scopus 로고
    • Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization
    • A. Forsgen, P. E. Gill, and J. R. Shinnerl, Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 187-211.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 187-211
    • Forsgen, A.1    Gill, P.E.2    Shinnerl, J.R.3
  • 15
    • 0032451351 scopus 로고    scopus 로고
    • Biomorphic cellular silicon carbide ceramics from wood: I. Processing and microstructure, and II. Mechanical properties
    • P. Greil, T. Lifka, and A. Kaindl, Biomorphic cellular silicon carbide ceramics from wood: I. Processing and microstructure, and II. Mechanical properties, J. Europ. Ceramic Soc., 18 (1998), pp. 1961-1973 and 1975-1983.
    • (1998) J. Europ. Ceramic Soc. , vol.18 , pp. 1961-1973-1975-1983
    • Greil, P.1    Lifka, T.2    Kaindl, A.3
  • 16
    • 1442285037 scopus 로고    scopus 로고
    • Primal-dual Newton-type interior-point method for topology optimization
    • R. H. W. Hoppe, S. I. Petrova, and V. Schulz, Primal-dual Newton-type interior-point method for topology optimization, J. Optimization Theory Appl., 114 (2002), No. 3, pp. 545-571.
    • (2002) J. Optimization Theory Appl. , vol.114 , Issue.3 , pp. 545-571
    • Hoppe, R.H.W.1    Petrova, S.I.2    Schulz, V.3
  • 17
    • 23044529568 scopus 로고    scopus 로고
    • Structural optimization of biomorphic microcellular ceramics by homogenization approach
    • Springer
    • R. H. W. Hoppe and S. I. Petrova, Structural optimization of biomorphic microcellular ceramics by homogenization approach, Lect. Notes Comput. Sci., Springer, 2179 (2001), pp. 353-360.
    • (2001) Lect. Notes Comput. Sci. , vol.2179 , pp. 353-360
    • Hoppe, R.H.W.1    Petrova, S.I.2
  • 21
    • 0002781299 scopus 로고
    • Edited by N. Megiddo, Springer Verlag, New York, New York
    • M. Kojima, S. Mizuno, and A. Yoshise, A primal-dual method for linear programming, Progress in Mathematical Programming, Interior Point and Related Methods (1989), Edited by N. Megiddo, Springer Verlag, New York, New York, pp. 29-47.
    • (1989) A primal-dual method for linear programming , pp. 29-47
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 22
    • 0020938409 scopus 로고
    • On structural optimization
    • N. Olhoff and J. E. Taylor, On structural optimization, J. Appl. Mech., 50 (1983), pp. 1139-1151.
    • (1983) J. Appl. Mech. , vol.50 , pp. 1139-1151
    • Olhoff, N.1    Taylor, J.E.2
  • 24
    • 0001511481 scopus 로고
    • Some properties of the Hessian of the logatithmie barrier function
    • M. H. Wright, Some properties of the Hessian of the logatithmie barrier function, Math. Program., 67 (1994), pp. 265-295.
    • (1994) Math. Program. , vol.67 , pp. 265-295
    • Wright, M.H.1
  • 25
    • 0032237110 scopus 로고    scopus 로고
    • Ill-conditioning and computational error in interior methods for nonlinear programming
    • M. H. Wright, Ill-conditioning and computational error in interior methods for nonlinear programming, SIAM J. Optim., 9 (1998), pp. 84-111.
    • (1998) SIAM J. Optim. , vol.9 , pp. 84-111
    • Wright, M.H.1
  • 26
    • 0000287204 scopus 로고    scopus 로고
    • An interior-point algorithm for nonconvex nonlinear programming
    • R. J. Vanderbei and D. F. Shanno, An interior-point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl., 13 (1999), pp. 231-252.
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 231-252
    • Vanderbei, R.J.1    Shanno, D.F.2
  • 27
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • H. A. Van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 631-644
    • Van der Vorst, H.A.1
  • 28
    • 0002801220 scopus 로고
    • On the convergence of multigrid methods with transforming smoothers. Theory with applications to the Navier-Stokes equations
    • G. Wittum, On the convergence of multigrid methods with transforming smoothers. Theory with applications to the Navier-Stokes equations, Numer. Math., 57 (1989), pp. 15-38.
    • (1989) Numer. Math. , vol.57 , pp. 15-38
    • Wittum, G.1


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