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Quadratic Programming as an Extension of Classical Quadratic Maximization

Author

Listed:
  • H. Theil

    (Netherlands School of Economics, Econometric Institute)

  • C. Van De Panne

    (Netherlands School of Economics, Econometric Institute)

Abstract

The article describes a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities. First the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form. The constraints which are then violated are added in a similar way to the constraints already imposed. It is shown that under certain general conditions this procedure leads to the required optimum in a finite number of steps. The procedure is illustrated by an example while also a directory of computations is given.

Suggested Citation

  • H. Theil & C. Van De Panne, 1960. "Quadratic Programming as an Extension of Classical Quadratic Maximization," Management Science, INFORMS, vol. 7(1), pages 1-20, October.
    • Handle: RePEc:inm:ormnsc:v:7:y:1960:i:1:p:1-20
    DOI: 10.1287/mnsc.7.1.1
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    Cited by:

    1. Tapia-Ubeda, Francisco J. & Miranda, Pablo A. & Macchi, Marco, 2018. "A Generalized Benders Decomposition based algorithm for an inventory location problem with stochastic inventory capacity constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 806-817.
    2. van den Berg, Gerard J., 2007. "On the uniqueness of optimal prices set by monopolistic sellers," Journal of Econometrics, Elsevier, vol. 141(2), pages 482-491, December.

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