A Projected Conjugate Gradient Method for Sparse Minimax Problems.

Kaj Madsen, Kristjan Jonasson

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    A new method for nonlinear minimax problems is presented. The method is of the trust region type and based on sequential linear programming. It is a first order method that only uses first derivatives and does not approximate Hessians. The new method is well suited for large sparse problems as it only requires that software for sparse linear programming and a sparse symmetric positive definite equation solver are available. On each iteration a special linear/quadratic model of the function is minimized, but contrary to the usual practice in trust region methods the quadratic model is only defined on a one dimensional path from the current iterate to the boundary of the trust region. Conjugate gradients are used to define this path. One iteration involves one LP subproblem and requires three function evaluations and one gradient evaluation. Promising numerical results obtained with the method are presented. In fact, we find that the number of iterations required is comparable to that of state-of-the-art quasi-Newton codes.
    Original languageEnglish
    Title of host publicationProc. Symp. on Applied Mathematical Programming and Modelling. |Budapest.
    Publication date1993
    Pages304-311
    Publication statusPublished - 1993
    EventProc. Symp. on Applied Mathematical Programming and Modelling. - Budapest.
    Duration: 1 Jan 1993 → …

    Conference

    ConferenceProc. Symp. on Applied Mathematical Programming and Modelling.
    CityBudapest.
    Period01/01/1993 → …

    Keywords

    • sparse problems
    • minimax optimization

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