Abstract
Large-scale design optimization problems frequently require the exploitation of structure in order to obtain efficient and reliable solutions. Successful algorithms for general nonlinear programming problems with theoretical underpinnings do not usually accommodate any additional structure within the problem. In this article modifications are made to a trust region algorithm to take advantage of hierarchical structure without compromising the theoretical properties of the original algorithm.
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Conn, A.R.; Gould, N.I.M.; Toint, P.L. 1992:LANCELOT, A FORTRAN package for large-scale nonlinear optimization. Berlin, Heidelberg, New York: Springer
Fletcher, R. 1981: Second order corrections for nondifferentiable optimization. In: Watson, G.A. (ed.)Numerical analysis, Dundee 1981, pp. 85–115. Berlin, Heidelberg, New York: Springer
Griewank, A. 1991: The global convergence of partitioned BFGS on problems with convex decompositions and Lipschitzian gradients.Math. Prog. 50, 141–175
Griewank, A.; Toint, P.L. 1982a: Local convergence analysis for partitioned quasi-Newton updates.Numerische Mathematik 39, 429–448
Griewank, A.; Toint, P.L. 1982b: Partitioned variable metric updates for large structured optimization problems.Numerische Mathematik 39, 119–137
Krishnamachari, R. 1996:A decomposition synthesis methodology for optimal system design. Ph.D. Thesis, University of Michigan, Ann Arbor
Krishnamachari, R.; Papalambros, P.Y. 1997: A decomposition synthesis methodology for optimal system design.ASME J. Mech. Des. (to appear)
Michelena, N.; Papalambros, P.Y. 1995: Optimal model-based decomposition of powertrain system design.ASME J. Mech. Des. 117, 499–505
Nelson, S.A., II 1997:Optimal hierarchical system design via sequentially decomposed programming. Ph.D. Thesis, The University of Michigan, Ann Arbor
Nelson, S.A., II; Papalambros, P.Y. 1997: Sequentially decomposed programming.AIAA J. 35, 1209–1216
Padula, S.L.; Alexandrov, N.; Green, L.L. 1996: MDO test suite at NASA Langley Research Center. In:Proc. 6-th AIAA/NASA/ISSMO Symp. on Multipdisciplinary Analysis and Optimization (held in Bellevue, WA), pp. 410–420. AIAA
Papalambros, P.Y. 1995: Optimal design of mechanical engineering systems.ASME J. Mech. Des. 117, 55–62
Powell, M.J.D. 1975: Convergence properties of a class of minimization algorithms. In:Mangasarian, O.L.; Meyer, R.R.; Robinson, S.M. (eds.)Nonlinear programming 2, pp. 1–27. New York: Academic Press
Sobieszczanski-Sobieski, J.; James, B.B.; Riley, M.F. 1987: Structural sizing by generalized multilevel optimization.AIAA J. 25, 139–145
Thareja, R.R.; Haftka, R.T. 1990: Efficient single-level solution of hierarchical problems in structural optimization.AIAA J. 28, 506–514
Yuan, Y.-X. 1984: An example of only linearly convergence of trust region algorithms for nonsmooth optimization.IMA J. Numer. Anal. 4, 327–335
Yuan, Y.-X. 1995: On the convergence of a new trust region algorithm.Numerische Mathematik 70, 515–539
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Nelson, S.A., Papalambros, P.Y. A modified trust region algorithm for hierarchical NLP. Structural Optimization 16, 19–28 (1998). https://doi.org/10.1007/BF01213996
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DOI: https://doi.org/10.1007/BF01213996