On volumes of bounded convex sets

Rosalind Elster

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    For the n-dimensional golden search method used to solve a constrained optimization problem with a bounded closed convex feasible set X in the n-dimensional Euclidean space, one can evaluate the number of computations of the objective values. This evaluation requires, however, a search for a lower bound for the volume of X which is based on elementary geometrical facts. In this connection, one can observe that the closedness condition with respect to X need not be assumed. If we apply the obtained results to an n-simplex S for which every vertex has distance h to the being opposite bounding hyperplane, then S turns out to be a bounded convex set with minimal volume. © 2010 Taylor & Francis.
    Original languageEnglish
    Pages (from-to)141-146
    JournalOptimization
    Volume59
    Issue number1
    DOIs
    Publication statusPublished - 19 Feb 2010

    Keywords

    • Golden search method
    • Nonlinear optimization
    • Symmetrization of bounded convex sets
    • Volume of bounded convex sets

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