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

Willard I. Zangwill
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Willard I. Zangwill: University of California Berkeley

Management Science, 1967, vol. 14, issue 1, 58-78

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.

Date: 1967
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:14:y:1967:i:1:p:58-78

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