Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Optimality conditions in generalized geometric programming

  • 55 Accesses

  • 7 Citations


Generalizations of the Kuhn-Tucker optimality conditions are given, as are the fundamental theorems having to do with their necessity and sufficiency.

This is a preview of subscription content, log in to check access.


  1. 1.

    Peterson, E. L.,Geometric Programming, SIAM Review, Vol. 18, pp. 1–51, 1976.

  2. 2.

    Halkin, H., andNeustadt, L. W.,General Necessary Conditions for Optimization Problems, Proceedings of the National Academy of Sciences, Vol. 29, pp. 422–435, 1966.

  3. 3.

    Guignard, M.,Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in Banach Space, SIAM Journal on Control, Vol. 7, pp. 232–241, 1969.

  4. 4.

    Luenberger, D. L.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.

  5. 5.

    Neustadt, L. W.,A General Theory of Extremals, Journal of Computer Systems and Science, Vol. 3, pp. 12–65, 1969.

  6. 6.

    Holmes, R. B.,A Course on Optimization and Best Approximation, Springer-Verlag, Heidelberg, Germany, 1972.

  7. 7.

    Bazarra, M., andGoode, W.,Necessary Optimality Criteria in Mathematical Programming in the Presence of Differentiability, Journal of Mathematical Analysis and Applications, Vol. 40, pp. 16–23, 1972.

  8. 8.

    Luenberger, D. L.,Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973.

  9. 9.

    Peterson, E. L.,Lagrangian Saddle Points and Duality in Generalized Geometric Programming, Journal of Optimization Theory and Applications, Vol. 26, No. 1, 1978.

Download references

Author information

Additional information

This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-73-2516.

Communicated by M. Avriel

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Peterson, E.L. Optimality conditions in generalized geometric programming. J Optim Theory Appl 26, 3–13 (1978).

Download citation

Key Words

  • Optimality conditions
  • geometric programming
  • nonlinear programming
  • ordinary programming
  • Kuhn-Tucker conditions