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Extension of Bolzano search to rectangles which preserves rectangles as iterates

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  • Marvin D. Troutt

Abstract

Multivariable elimination algorithms, which may be regarded as generalizations of various one‐dimensional search procedures, have not found wide application. A probable reason may be the generally very irregularly shaped regions of uncertainty that evolve iteratively in the procedures. Hence hope for practical salvage of this class of algorithms seems to lie in controlling the shape of the successively smaller regions of uncertainty. In this article an extension of Bolzano search to rectangles which preserves rectangular iterates is given. Since the result is essentially geometrical in nature, a geometric proof of this procedure is given. Hopefully the proof procedure will be of independent interest. A numerical illustration of the procedure is given for a game problem, such problems lending themselves to this method.

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  • Marvin D. Troutt, 1987. "Extension of Bolzano search to rectangles which preserves rectangles as iterates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 593-603, August.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:4:p:593-603
    DOI: 10.1002/1520-6750(198708)34:43.0.CO;2-H
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    Cited by:

    1. Troutt, Marvin D. & Leung, T. W., 2003. "Enhanced bisection strategies for the Maximin Efficiency Ratio model," European Journal of Operational Research, Elsevier, vol. 144(3), pages 545-553, February.

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