Abstract
It is shown that certain theorems concerning differentiable pseudoconvex functions can be extended to a class of nondifferentiable pseudoconvex functions that was defined with help of the Dini-derivative by Diewert recently.
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References
J.-P. Crouzeix and J.A. Ferland, “Criteria for quasi-convexity and pseudoconvexity: Relationships and comparisons”,Mathematical Programming 23 (1982) 193–205.
J.-P. Crouzeix “Sur l'existence de la dérivée des fonctions quasiconvexes”, Séminaire analyse numerique et optimasation, Université de Clermont II (Novembre 1979).
J.-P. Crouzeix. Some differentiability properties of quasiconvex functions onR”, in eds. A. Auslender, W. Oettli and J. Stoer,Optimization and optimal control (Proceedings of a conference held at Oberwolfach March 16–22. 1980) Springer-Verlag, Berlin (1981).
W.E. Diewert, ⨑Alternative characterizations of six kinds of quasiconcavity in the nondifferentiable case with applications to nonsmooth programming”, in: S. Schaible and W.T. Ziemba, eds.,Generalized concavity to optimization and economics (Academic Press, New York, 1981) pp. 51–93.
J.B. Hiriart-Urruty, “New concepts in nondifferentiable programming”, Journées d'analyse non convexe, Université de Pau (France, 1977).
O.L. Mangasarian, “Pseudo-convex functions”,SIAM Journal on Control 3 (1965) 281–290.
R. Mifflin, “Semismooth and semiconvex functions in optimization”,SIAM Journal on Control and Optimization 15 (1977) 959–972.
J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970).
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Komlósi, S. Some properties of nondifferentiable pseudoconvex functions. Mathematical Programming 26, 232–237 (1983). https://doi.org/10.1007/BF02592057
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DOI: https://doi.org/10.1007/BF02592057