Optimizing partially separable functions without derivatives

B. Colson, Philippe Toint

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    Abstract

    We present an algorithm for solving nonlinear programming problems involving a partially separable objective function whose derivatives are assumed to be unavailable. At each iteration, we construct a quadratic interpolation model of the objective function around the current iterate and minimize this model to obtain a trial step. The whole process is embedded within a trust-region framework. We further propose to use ideas of Curtis, Powell and Reid to minimize the number of calls to the objective function in the part of the derivative-free algorithm that improves the geometry of the interpolation set. Numerical experiments tend to confirm the promising behaviour of the algorithm. © 2005 Taylor & Francis Group Ltd.
    Original languageEnglish
    Pages (from-to)493-508
    Number of pages16
    JournalOptimization Methods and Software
    Volume20
    Issue number4-5
    DOIs
    Publication statusPublished - 1 Aug 2005

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