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A lagrangian property for homogeneous programs

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Abstract

Euler's equation is applied to the response function of a mathematical program whose maximand and constraint functions are positively homogeneous over the policy cone. An algorithmic advantage (using GLM) is cited, and certain posynomial geometric programs are distinguished.

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References

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    Nunn, W.,The Lagrange Multiplier—A Heuristic Presentation, Center for Naval Analysis, Operations Evaluation Group, Report No. 76, 1966.

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

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    Duffin, R.,Linearizing Geometric Programs, SIAM Review, Vol. 12, pp. 211–227, 1970.

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Communicated by G. L. Nemhauser

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Greenberg, H.J. A lagrangian property for homogeneous programs. J Optim Theory Appl 12, 99–102 (1973). https://doi.org/10.1007/BF00934838

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Keywords

  • Constraint Function
  • Geometric Program
  • Single Constraint
  • Policy Cone
  • Lagrangian Property