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Volumn 37, Issue 4, 1999, Pages 1070-1088

Newton's mesh independence principle for a class of optimal shape design problems

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONTROL SYSTEM SYNTHESIS; PROBLEM SOLVING;

EID: 0032688739     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996303529     Document Type: Article
Times cited : (18)

References (40)
  • 1
    • 0001295889 scopus 로고
    • Optimal design for minimum weight and compliance in plane stress using extremal microstructures
    • G. ALLAIRE AND R. V. KOHN, Optimal design for minimum weight and compliance in plane stress using extremal microstructures, European J. Mech. A Solids, 12 (1993), pp. 839-878.
    • (1993) European J. Mech. A Solids , vol.12 , pp. 839-878
    • Allaire, G.1    Kohn, R.V.2
  • 2
    • 0023577191 scopus 로고
    • Application of the mesh independence principle to mesh refinement strategies
    • E. L. ALLGOWER AND K. BÖHMER, Application of the mesh independence principle to mesh refinement strategies, SIAM J. Numer. Anal., 24 (1987), pp. 1335-1351.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1335-1351
    • Allgower, E.L.1    Böhmer, K.2
  • 3
    • 0022661397 scopus 로고
    • A mesh-independence principle for operator equations and their discretizations
    • E. L. ALLGOWER, K. BÖHMER, F.-A. POTRA, AND W. C. RHEINBOLDT, A mesh-independence principle for operator equations and their discretizations, SIAM J. Numer. Anal., 23 (1986), pp. 160-169.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 160-169
    • Allgower, E.L.1    Böhmer, K.2    Potra, F.-A.3    Rheinboldt, W.C.4
  • 5
    • 0024170217 scopus 로고
    • Boundary identification for 2-d parabolic problems arising in thermal testing of materials
    • Austin, TX
    • H. T. BANKS AND F. KOJIMA, Boundary identification for 2-d parabolic problems arising in thermal testing of materials, in Proc. of the 27th Conference on Decision and Control, Austin, TX, 1988, pp. 1678-1683.
    • (1988) Proc. of the 27th Conference on Decision and Control , pp. 1678-1683
    • Banks, H.T.1    Kojima, F.2
  • 7
    • 0003563178 scopus 로고
    • Stable solution of inverse problems
    • Friedr. Vieweg & Sohn, Braunschweig
    • J. BAUMEISTER, Stable Solution of Inverse Problems, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1987.
    • (1987) Advanced Lectures in Mathematics
    • Baumeister, J.1
  • 8
    • 0016626491 scopus 로고
    • Application de la méthode des éléments finis à l'approximation d'un problème de domain optimal
    • D. BEGIS AND R. GLOWINSKI, Application de la méthode des éléments finis à l'approximation d'un problème de domain optimal, Appl. Math. Comput., 2 (1975), pp. 130-169.
    • (1975) Appl. Math. Comput. , vol.2 , pp. 130-169
    • Begis, D.1    Glowinski, R.2
  • 10
    • 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
  • 11
    • 84973957248 scopus 로고
    • Approximation of young measures by functions and application to a problem of optimal design for plates with variable thickness
    • E. BONNETIER AND C. CONCA, Approximation of Young measures by functions and application to a problem of optimal design for plates with variable thickness, Proc. Roy. Soc. Edinburgh Sect. A, 124 (1994), pp. 399-422.
    • (1994) Proc. Roy. Soc. Edinburgh Sect. A , vol.124 , pp. 399-422
    • Bonnetier, E.1    Conca, C.2
  • 12
    • 0028380746 scopus 로고
    • Discrete gradient and discretized continuum gradient method for shape optimization of shells
    • D. CHENAIS, Discrete gradient and discretized continuum gradient method for shape optimization of shells, Mech. Structures Mach., 22 (1994), pp. 73-115.
    • (1994) Mech. Structures Mach. , vol.22 , pp. 73-115
    • Chenais, D.1
  • 13
    • 8544220284 scopus 로고
    • Basic error estimates for elliptic problems
    • P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam
    • P. G. CIARLET, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis. Vol. II, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991, pp. 17-351.
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 17-351
    • Ciarlet, P.G.1
  • 14
    • 0020589624 scopus 로고
    • Optimal design of a minimum weight thermal diffuser with constraint on the output thermal power flux
    • M. DELFOUR, G. PAYRE, AND J.-P. ZOLÉSIO, Optimal design of a minimum weight thermal diffuser with constraint on the output thermal power flux, Appl. Math. Optim., 9 (1983), pp. 225-262.
    • (1983) Appl. Math. Optim. , vol.9 , pp. 225-262
    • Delfour, M.1    Payre, G.2    Zolésio, J.-P.3
  • 19
    • 0009552037 scopus 로고
    • Control/fictitious domain method for solving optimal shape design problems
    • J. HASLINGER, K.-H. HOFFMANN, AND M. KOČVARA, Control/fictitious domain method for solving optimal shape design problems, RAIRO Modél. Math. Anal. Numér., 27 (1993), pp. 157-182.
    • (1993) RAIRO Modél. Math. Anal. Numér. , vol.27 , pp. 157-182
    • Haslinger, J.1    Hoffmann, K.-H.2    Kočvara, M.3
  • 22
    • 0000409919 scopus 로고
    • Mesh independence for nonlinear least squares problems with norm constraints
    • M. HEINKENSCHLOSS, Mesh independence for nonlinear least squares problems with norm constraints, SIAM J. Optim., 3 (1993), pp. 81-117.
    • (1993) SIAM J. Optim. , vol.3 , pp. 81-117
    • Heinkenschloss, M.1
  • 25
    • 0039677529 scopus 로고
    • Thin plates with varying thicknesses and their relation to structural optimization
    • J. L. Ericksen et al., eds., Springer-Verlag, New York
    • R. V. KOHN AND M. VOGELIUS, Thin plates with varying thicknesses and their relation to structural optimization, in Homogenization and Effective Moduli of Materials and Media, IMA Vol. Math. Appl. 1, J. L. Ericksen et al., eds., Springer-Verlag, New York, 1986, pp. 126-149.
    • (1986) Homogenization and Effective Moduli of Materials and Media, IMA Vol. Math. Appl. , vol.1 , pp. 126-149
    • Kohn, R.V.1    Vogelius, M.2
  • 26
    • 0002886450 scopus 로고
    • Mesh independence of Newton-like methods for infinite-dimensional problems
    • C. T. KELLEY AND E. W. SACHS, Mesh independence of Newton-like methods for infinite-dimensional problems, J. Integral Equations Appl., 3 (1991), pp. 549-573.
    • (1991) J. Integral Equations Appl. , vol.3 , pp. 549-573
    • Kelley, C.T.1    Sachs, E.W.2
  • 27
    • 0007020143 scopus 로고
    • Broyden's method for approximate solution of nonlinear integral equations
    • C. T. KELLEY AND E. W. SACHS, Broyden's method for approximate solution of nonlinear integral equations, J. Integral Equations Appl., 9 (1985), pp. 25-44.
    • (1985) J. Integral Equations Appl. , vol.9 , pp. 25-44
    • Kelley, C.T.1    Sachs, E.W.2
  • 28
    • 0023451450 scopus 로고
    • Quasi-Newton methods and unconstrained optimal control problems
    • C. T. KELLEY AND E. W. SACHS, Quasi-Newton methods and unconstrained optimal control problems, SIAM J. Control Optim., 25 (1987), pp. 1503-1516.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 1503-1516
    • Kelley, C.T.1    Sachs, E.W.2
  • 29
    • 0025404331 scopus 로고
    • Approximate quasi-Newton methods
    • C. T. KELLEY AND E. W. SACHS, Approximate quasi-Newton methods, Math. Programming, 48 (1990), pp. 41-70.
    • (1990) Math. Programming , vol.48 , pp. 41-70
    • Kelley, C.T.1    Sachs, E.W.2
  • 30
    • 85038068752 scopus 로고    scopus 로고
    • A comparison of numerical methods for optimal shape design problems
    • to appear
    • M. LAUMEN, A comparison of numerical methods for optimal shape design problems, Optim. Methods Softw., to appear.
    • Optim. Methods Softw.
    • Laumen, M.1
  • 31
    • 85038059162 scopus 로고    scopus 로고
    • Newton's method for a class of optimal shape design problems
    • to appear
    • M. LAUMEN, Newton's method for a class of optimal shape design problems, SIAM J. Optim., to appear.
    • SIAM J. Optim.
    • Laumen, M.1
  • 33
    • 0001496391 scopus 로고    scopus 로고
    • Calcul des variations et homogénéisation
    • Les méthodes de l'homogénéisation: Théorie et applications en physique, D. Bergman et al., eds., Eyrolles, Paris
    • F. MURAT AND L. TARTAR, Calcul des variations et homogénéisation, in Les méthodes de l'homogénéisation: Théorie et applications en physique, D. Bergman et al., eds., Collection Dir. Etudes et Rech. Elec. France 57, Eyrolles, Paris, pp. 319-369.
    • Collection Dir. Etudes et Rech. Elec. France , vol.57 , pp. 319-369
    • Murat, F.1    Tartar, L.2
  • 34
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • C. C. PAIGE AND M. A. SAUNDERS, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal., 12 (1975), pp. 617-629.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 37
    • 0041338065 scopus 로고
    • An adaptive continuation process for solving systems of nonlinear equations
    • Banach Center Publ. 3, PWN, Warsaw
    • W. C. RHEINBOLDT, An adaptive continuation process for solving systems of nonlinear equations, in Mathematical Models and Numerical Methods, Banach Center Publ. 3, PWN, Warsaw, 1978, pp. 129-142.
    • (1978) Mathematical Models and Numerical Methods , pp. 129-142
    • Rheinboldt, W.C.1


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