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

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 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.