Abstract
A simplex-type method for finding a local maximum of [Formula: see text] subject to [Formula: see text] and [Formula: see text] is proposed. At a local maximum, the objective function (1), can be expressed, in terms of the non-basic variables λ0, as [Formula: see text] and the vector of partial derivatives of (13), with respect to the non-basic variables may be written, [Formula: see text] This allows calculation of the maximum values of the non-basic variables, increased one at a time, consistent with ∇Z ≧ 0. A “cutting plane” a**λ′ ≧ 1 is then defined which excludes the local optimum, and many lower values (but no higher values) of (1). The form of the square matrix C is immaterial.
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