Programming for Sparse Minimax Optimization

K. Jonasson, Kaj Madsen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We present an algorithm for nonlinear minimax optimization which is well suited for large and sparse problems. The method is based on trust regions and sequential linear programming. On each iteration, a linear minimax problem is solved for a basic step. If necessary, this is followed by the determination of a minimum norm corrective step based on a first-order Taylor approximation. No Hessian information needs to be stored. Global convergence is proved. This new method has been extensively tested and compared with other methods, including two well known codes for nonlinear programming. The numerical tests indicate that in many cases the new method can find the solution in just as few iterations as methods based on approximate second-order information. The tests also show that for some problems the corrective steps give much faster convergence than for similar methods which do not employ such steps
    Original languageEnglish
    JournalBIT
    Volume34
    Issue number3
    Pages (from-to)372-388
    Publication statusPublished - 1994

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