Abstract
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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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
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DOI: https://doi.org/10.1007/BF00934352