Mathematical Programming

, Volume 11, Issue 1, pp 283–290 | Cite as

Fractional programming without differentiability

  • J. M. Borwein
Article

Abstract

The notion of quasi-differentiability is examined and related to fractional programming. Necessary and sufficient conditions are given and various other properties of quasi-differentiable functions are discussed. Differentiability is not assumed.

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References

  1. [1]
    C.R. Bector, “Duality in nonlinear fractional programming”,Zeitschrift für Operations Research 17 (1973) 183–193.Google Scholar
  2. [2]
    F.E. Browder, “Nonlinear maximal monotone operators in banach space”,Mathematische Annalen 175 (1968) 89–113.Google Scholar
  3. [3]
    R. Jagannathan, “Duality for nonlinear fractional programs”,Zeitschrift für Operations Research 17, (1973), 1–3.Google Scholar
  4. [4]
    C.J. Minty, “On the monotonicity of the gradient of a convex function”,Pacific Journal of Mathematics 14 (1964) 243–247.Google Scholar
  5. [5]
    J. Ponstein, “Seven kinds of convexity”,SIAM Review 2 (1967) 115–119.Google Scholar
  6. [6]
    B.N. Pshenichnyi,Necessary conditions for an extremum, (Marcel Dekker, New York, 1971).Google Scholar
  7. [7]
    R.T. Rockafellar,Convex analysis (Princeton Univ. Press, Princeton, N.J., 1970).Google Scholar
  8. [8]
    S. Schaible, “Parameter-free convex equivalent and dual programs of fractional programming problems”,Zeitschrift für Operations Research 18 (1974) 187–196.Google Scholar
  9. [9]
    P. Wolfe, “A duality theorem for non-linear programming”,Quarterly of Applied Mathematics 19 (1961) 239–244.Google Scholar

Copyright information

© The Mathematical Programming Society 1976

Authors and Affiliations

  • J. M. Borwein
    • 1
  1. 1.Dalhousie UniversityHalifaxCanada

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