A simplex-type method for finding a local maximum of
subject to
and
is proposed. At a local maximum, the objective function (1), can be expressed, in terms of the non-basic variables λ
0, as
and the vector of partial derivatives of (13), with respect to the non-basic variables may be written,
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.
