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Some exact iterative procedures for finding the puncture point of a convex set

  • M. C. Spruill
Contributed Papers
  • 40 Downloads

Abstract

LetK be a convex set in the Hilbert spaceH, and let the ray {αc: α ∈R} punctureK at β*c. Some algorithms are given for finding β*. Each algorithm results in a nonincreasing sequence {β i } which converges to β*. The points βjc lie in successive supporting hyperplanes toK. The normal to thenth hyperplane is obtained by a minimization over a set no larger than the unitn cube. It is assumed that the subset ofK which maximizes (φ,x) forx inK is found relatively easily.

Key Words

Convex sets supporting hyperplanes minimax points optimal experimental design 

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References

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    Karlin, S., andStudden, W. J.,Optimal Experimental Designs, Annals of Mathematical Statistics, Vol. 37, 1966.Google Scholar
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    Fedorov, V. V.,Theory of Optimal Experiments, Academic Press, New York, New York, 1972.Google Scholar
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    Atwood, C. L.,Convergent Design Sequences for Sufficiently Regular Optimality Criteria, Annals of Statistics, Vol. 4, No. 6, 1976.Google Scholar
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    Gribik, P. R., andKortanek, K. O.,Equivalence Theorems and Cutting Plane Algorithms for a Class of Experimental Design Problems, SIAM Journal on Applied Mathematics, Vol. 32, No. 1, 1977.Google Scholar
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    Studden, W. J., andTsay, J. Y.,Remez's Procedure for Finding Optimal Designs, Annals of Statistics, Vol. 4, No. 6, 1976.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • M. C. Spruill
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlanta

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