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

Author

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  • Wilfred Candler

    (Massey University College of Manawatu, New Zealand)

  • Robert J. Townsley

    (Massey University College of Manawatu, New Zealand)

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.

Suggested Citation

  • Wilfred Candler & Robert J. Townsley, 1964. "The Maximization of a Quadratic Function of Variables Subject to Linear Inequalities," Management Science, INFORMS, vol. 10(3), pages 515-523, April.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:3:p:515-523
    DOI: 10.1287/mnsc.10.3.515
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