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Technical Note—“Linear” Programming with Absolute-Value Functionals

Author

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  • David F. Shanno

    (University of Toronto, Toronto, Ontario, Canada)

  • Roman L. Weil

    (University of Chicago, Chicago, Illinois)

Abstract

Consider the problem Ax = b ; max z = ∑ c j | x j |. This problem cannot, in general, be solved with the simplex method. The problem has a simplex-method solution (with unrestricted basis entry) only if c j are nonpositive (nonnegative for minimizing problems).

Suggested Citation

  • David F. Shanno & Roman L. Weil, 1971. "Technical Note—“Linear” Programming with Absolute-Value Functionals," Operations Research, INFORMS, vol. 19(1), pages 120-124, February.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:1:p:120-124
    DOI: 10.1287/opre.19.1.120
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    Cited by:

    1. Yoonsik Hong & Yanghoon Kim & Jeonghun Kim & Yongmin Choi, 2022. "Index Tracking via Learning to Predict Market Sensitivities," Papers 2209.00780, arXiv.org, revised Dec 2022.

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