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A general multiplier rule

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Abstract

An extension of a general multiplier rule derived by Gittleman, which in turn is an extension of a theorem due to Hestenes, is proved. The extension requires a less complicated definition of derived set.

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References

  1. 1.

    Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, New York, 1966.

  2. 2.

    Gittleman, A.,A General Multiplier Rule, Journal of Optimization Theory and Applications, Vol. 7, No. 1, 1971.

  3. 3.

    Tuy, H.,On the Convex Approximation of Nonlinear Inequalities, Mathematische Operationsforschung und Statistik, Vol. 5, No. 6, 1974.

  4. 4.

    Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.

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Communicated by M. R. Hestenes

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Cite this article

Nieuwenhuis, J.W. A general multiplier rule. J Optim Theory Appl 31, 167–176 (1980). https://doi.org/10.1007/BF00934108

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Key Words

  • Mathematical programming
  • multiplier rule
  • derived set
  • linearization theorem