Philon's line generalized: an optimization problem from geometry

Wolfgang Wetterling

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    Abstract

    Consider inn-dimensional Euclidean space the intersection of a convex cone and a hyperplane through a given point. The problem is to minimize the (n-1)-volume of this intersection. A geometric interpretation of the first-order optimality condition is given. The special casen=2 is known as a characteristic property of Philon's line.
    Original languageEnglish
    Pages (from-to)517-521
    Number of pages5
    JournalJournal of optimization theory and applications
    Volume90
    Issue number3
    DOIs
    Publication statusPublished - 1996

    Keywords

    • Philon's line
    • Centroids
    • Optimality conditions
    • Convex cones

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