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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C.R. Bector, “Duality in nonlinear fractional programming”,Zeitschrift für Operations Research 17 (1973) 183–193.
F.E. Browder, “Nonlinear maximal monotone operators in banach space”,Mathematische Annalen 175 (1968) 89–113.
R. Jagannathan, “Duality for nonlinear fractional programs”,Zeitschrift für Operations Research 17, (1973), 1–3.
C.J. Minty, “On the monotonicity of the gradient of a convex function”,Pacific Journal of Mathematics 14 (1964) 243–247.
J. Ponstein, “Seven kinds of convexity”,SIAM Review 2 (1967) 115–119.
B.N. Pshenichnyi,Necessary conditions for an extremum, (Marcel Dekker, New York, 1971).
R.T. Rockafellar,Convex analysis (Princeton Univ. Press, Princeton, N.J., 1970).
S. Schaible, “Parameter-free convex equivalent and dual programs of fractional programming problems”,Zeitschrift für Operations Research 18 (1974) 187–196.
P. Wolfe, “A duality theorem for non-linear programming”,Quarterly of Applied Mathematics 19 (1961) 239–244.
Author information
Authors and Affiliations
Additional information
This research was partially supported by N.R.C. Grants A7751 and A7675.
Rights and permissions
About this article
Cite this article
Borwein, J.M. Fractional programming without differentiability. Mathematical Programming 11, 283–290 (1976). https://doi.org/10.1007/BF01580396
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01580396