A conjugate gradient quasi-newton method for structural optimisation

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    Abstract

    Structural optimisation involves the constrained minimisation of functions or functionals and the majority of the methods employed utilise in some manner algorithms developed for unconstrained optimisation. Two unconstrained optimisation methods of historical and current significance are the conjugate gradient method and the quasi-Newton method. The conjugate gradient method in particular remains a popular technique in optimisation practice because of its simplicity and rapid convergence for well-conditioned problems. Both the conjugate gradient and quasi-Newton method offer quadratic termination, i.e. for exact arithmetic and an n-dimensional problem both methods will converge in a maximum of n steps. This paper is concerned with assessing the performance of a combined conjugate gradient and quasi-Newton method for a number of relatively simple non-linear structural optimisation problems. The problems considered are designed to be poorly conditioned as the new method is shown to be particularly adept at solving these types of problems. The features of the new method are quadratic termination and that matrix updating is present, similar to the quasi-Newton method. However, this latter feature is optional and if no updating takes place the method reduces to the standard conjugate gradient method whilst if full updating is performed the quasi-Newton method is obtained. It is shown in the paper that best performance is obtained with partial updating and the extent depends on the ill-conditioning of the problem.
    Original languageEnglish
    Title of host publicationProceedings of the 8th International Conference on Computational Structures Technology, CST 2006
    PublisherCivil-Comp Press
    Volume83
    ISBN (Print)9781905088089
    Publication statusPublished - 1 Jan 2006
    Event8th International Conference on Computational Structures Technology, CST 2006 - Las Palmas de Gran Canaria, Spain
    Duration: 12 Sep 200615 Sep 2006

    Publication series

    NameCivil-Comp Proceedings
    PublisherCivil-Comp Press
    ISSN (Print)1759-3433

    Conference

    Conference8th International Conference on Computational Structures Technology, CST 2006
    Country/TerritorySpain
    CityLas Palmas de Gran Canaria
    Period12/09/0615/09/06

    Keywords

    • Conjugate gradients
    • Optimisation
    • Quasi-Newton
    • Structural

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