A note on the convergence of barrier algorithms to second-order necessary points

Nick Gould, Philippe Toint

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    Abstract

    It has long been known that barrier algorithms for constrained optimization can produce a sequence of iterates converging to a critical point satisfying weak second-order necessary optimality conditions, when their inner iterations ensures that second-order necessary conditions hold at each barrier minimizer. We show that, despite this, strong second-order necessary conditions may fail to be attained at the limit, even if the barrier minimizers satisfy second-order sufficient optimality conditions.
    Original languageEnglish
    Pages (from-to)433-438
    Number of pages6
    JournalMathematical Programming
    Volume85
    Issue number2
    DOIs
    Publication statusPublished - 1 Jan 1999

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