Singularities in minimax optimization of networks

Kaj Madsen, Hans Schjær-Jacobsen

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    A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems.
    Original languageEnglish
    JournalIEEE Transactions on Circuits and Systems
    Issue number7
    Pages (from-to)456-460
    Publication statusPublished - 1976

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    Copyright: 1976 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE


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