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An Algorithm for the Chebyshev Problem--With an Application to Concave Programming

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  • Willard I. Zangwill

    (University of California Berkeley)

Abstract

The Chebyshev problem is to determine a point x \alpha which solves max \alpha min i - 1,..., N{g i (x)}. By exploiting generalized inverses an algorithm is developed for determining x \alpha . It is also shown that in a certain sense the Chebyshev problem is equivalent to the concave programming problem. Moreover, for the programming problem generated by the Chebyshev problem, the Kuhn-Tucker conditions are proven to be sufficient even though the feasible region may not be convex.

Suggested Citation

  • Willard I. Zangwill, 1967. "An Algorithm for the Chebyshev Problem--With an Application to Concave Programming," Management Science, INFORMS, vol. 14(1), pages 58-78, September.
  • Handle: RePEc:inm:ormnsc:v:14:y:1967:i:1:p:58-78
    DOI: 10.1287/mnsc.14.1.58
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