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Differential Calculus in Nonlinear Programming

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  • Douglass J. Wilde

    (Department of Chemical Engineering, The University of Texas, Austin 12, Texas)

Abstract

Using only well-known theorems of the differential calculus, we derive necessary conditions for a relative minimum of a nonlinear differentiable objective function of nonnegative variables constrained by nonlinear differentiable inequalities. The results are expressed entirely in terms of partial derivatives, which are subsequently identified with the Lagrange multipliers of the Kuhn-Tucker nonlinear programming theorem. Our conditions may be considered therefore as the Kuhn-Tucker theorem in differential rather than Lagrangian form.

Suggested Citation

  • Douglass J. Wilde, 1962. "Differential Calculus in Nonlinear Programming," Operations Research, INFORMS, vol. 10(6), pages 764-773, December.
    • Handle: RePEc:inm:oropre:v:10:y:1962:i:6:p:764-773
    DOI: 10.1287/opre.10.6.764
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    Cited by:

    1. Kanti Swarup, 1968. "Note on linear fractional functionals programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 13(1), pages 72-77, December.

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