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Journal of Optimization Theory and Applications

, Volume 27, Issue 2, pp 291–299 | Cite as

A system of inequalities and nondifferentiable mathematical programming

  • C. Singh
Technical Note

Abstract

A system of inequalities involving nondifferentiable functions, originally introduced by Eisenberg, is extended. This result is then applied to establish optimality criteria and a dual theorem for a nondifferentiable mathematical program involving quasiconvexity in its equality constraints and inequality constraints. These are natural extensions of results recently established by Mond.

Key Words

Positive-semidefinite symmetric matrices optimality duality quasiconvexity 

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References

  1. 1.
    Eisenberg, E.,A Gradient Inequality for a Class of Nondifferentiable Functions, Operations Research, Vol. 14, pp. 157–163, 1966.Google Scholar
  2. 2.
    Mond, B.,A Class of Nondifferentiable Mathematical Programming Problems, Journal of Mathematical Analysis and Applications, Vol. 46, pp. 169–174, 1974.Google Scholar
  3. 3.
    Mond, B., andSchechter, M.,On a Constraint Qualification in a Nondifferentiable Programming Problem, Naval Research Logistics Quarterly, Vol. 23, pp. 611–613, 1976.Google Scholar
  4. 4.
    Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.Google Scholar
  5. 5.
    Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, Edited by J. Neyman, University of California Press, Berkeley, California, 1951.Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • C. Singh
    • 1
  1. 1.St. Lawrence UniversityCanton

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