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

David F. Shanno and Roman L. Weil
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David F. Shanno: University of Toronto, Toronto, Ontario, Canada
Roman L. Weil: University of Chicago, Chicago, Illinois

Operations Research, 1971, vol. 19, issue 1, 120-124

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).

Date: 1971
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