The Maximization of a Quadratic Function of Variables Subject to Linear Inequalities

Wilfred Candler and Robert J. Townsley
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Wilfred Candler: Massey University College of Manawatu, New Zealand
Robert J. Townsley: Massey University College of Manawatu, New Zealand

Management Science, 1964, vol. 10, issue 3, 515-523

Abstract: 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 \lambda 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 \nabla Z \geqq 0. A "cutting plane" a' \lambda' \geqq 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.

Date: 1964
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