This paper is devoted to the study of the different kinds of differentiability of quasiconvex functions onR n. For these functions, we show that Gâteaux-differentiability and Fréchet-differentiability are equivalent; we study the properties of the directional derivatives; and we show that if, for a quasiconvex function, the directional derivatives atx are all finite and two-sided, the function is differentiable atx.
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Newman, P.,Some Properties of Concave Functions, Journal of Economic Theory, Vol. 1, pp. 291–314, 1969.
Crouzeix, J. P.,Conditions for Convexity of Convex Functions, Mathematics of Operations Research, Vol. 5, pp. 120–125, 1980.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Crouzeix, J. P.,Contribution à l'Etude des Fonctions Quasiconvexes, Université de Clermont 2, Thèse de Docteur des Sciences, 1977.
Pshenichnyi, B. N.,Necessary Conditions for an Extremum, Marcel Dekker, New York, New York, 1971.
Borwein, J. M.,Fractional Programming without Differentiability, Mathematical Programming, Vol. 11, pp. 283–290, 1976.
Communicated by M. Avriel
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Crouzeix, J.P. About differentiability of order one of quasiconvex functions onR n . J Optim Theory Appl 36, 367–385 (1982). https://doi.org/10.1007/BF00934352
- Quasiconvex functions
- generalized convexity