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

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 λ 0 , 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.

• 저널Management Science · 10(3) · 515–523
• 토픽Statistical and numerical algorithms · Applied Mathematics
• DOI10.1287/mnsc.10.3.515
• 저자Wilfred Candler, Robert Townsley