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On “Pre-historic” Linear Programming and the Figure of the Earth

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  • Richard W. Cottle

    (Stanford University)

Abstract

An important scientific problem of the seventeenth and eighteenth centuries was to determine the figure of the earth. This problem attracted the attention of many notable people, one of whom was Roger Joseph Boscovich a Jesuit priest and natural scientist who formulated—and gave an algorithm for solving—linearly constrained optimization problems whose minimand is the sum of the absolute values of the errors, i.e., a special linear regression model. After first recounting some of the rich history of this development, the present expository note focuses on the method of Boscovich, exploring its interpretation as a variant of the simplex algorithm for linear programming applied to problems of that form.

Suggested Citation

  • Richard W. Cottle, 2017. "On “Pre-historic” Linear Programming and the Figure of the Earth," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 255-277, October.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:1:d:10.1007_s10957-017-1165-5
    DOI: 10.1007/s10957-017-1165-5
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    References listed on IDEAS

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    1. M. R. Rao & V. Srinivasan, 1972. "A Note on Sharpe's Algorithm for Minimizing the Sum of Absolute Deviations in a Simple Regression Problem," Management Science, INFORMS, vol. 19(2), pages 222-225, October.
    2. A. Charnes & W. W. Cooper & R. O. Ferguson, 1955. "Optimal Estimation of Executive Compensation by Linear Programming," Management Science, INFORMS, vol. 1(2), pages 138-151, January.
    3. William F. Sharpe, 1971. "Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios," Management Science, INFORMS, vol. 18(2), pages 1-13, October.
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