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The Convex Simplex Method

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  • Willard I. Zangwill

    (The University of California Berkeley)

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.

Suggested Citation

  • Willard I. Zangwill, 1967. "The Convex Simplex Method," Management Science, INFORMS, vol. 14(3), pages 221-238, November.
    • Handle: RePEc:inm:ormnsc:v:14:y:1967:i:3:p:221-238
    DOI: 10.1287/mnsc.14.3.221
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    Cited by:

    1. Hong Zheng, 2015. "Adaptation of Network Simplex for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 49(3), pages 543-558, August.
    2. Renaud Chicoisne, 2023. "Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes," Computational Optimization and Applications, Springer, vol. 84(3), pages 789-831, April.

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