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- W2092677228 abstract "Modern barrier methods for constrained optimization are sometimes portrayed conceptually as a sequence of inexact minimizations, with only a very few Newton iterations (perhaps just one) for each value of the barrier parameter. Unfortunately, this rosy image does not accurately reflect reality when the barrier parameter is reduced at a reasonable rate, as in a practical (long-step) method. Local analysis is presented indicating why a pure Newton step in a typical long-step barrier method for nonlinearly constrained optimization may be seriously infeasible, even when taken from an apparently favorable point; hence accurate calculation of the Newton direction does not guarantee an effective algorithm. The features described are illustrated numerically and connected to known theoretical results for well-behaved convex problems satisfying common assumptions such as self-concordancy. The contrasting nature of an approximate step to the desired minimizes of the barrier function is also discussed." @default.
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- W2092677228 date "1995-02-01" @default.
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- W2092677228 title "Why a Pure Primal Newton Barrier Step May be Infeasible" @default.
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- W2092677228 doi "https://doi.org/10.1137/0805001" @default.
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