The Convex Simplex Method

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

Management Science, 1967, vol. 14, issue 3, 221-238

Abstract: This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection techniques are used. With a linear objective function the convex simplex method reduces to the linear simplex method. Moreover, the convex simplex method actually behaves like the linear simplex method whenever it encounters a linear portion of a convex objective function. Many of the sophisticated techniques designed to enhance the efficiency of the linear simplex method are applicable to the convex simplex method. In particular, as an example, a network transportation problem with a convex objective function is solved by using the standard transportation tableau and by only slightly modifying the usual procedure for a linear objective function.

Date: 1967
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:14:y:1967:i:3:p:221-238

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