Abstract
Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexificators to be minimal. A characterization of quasiconvexity of a continuous function is obtained in terms of the quasimonotonicity of convexificators.
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Jeyakumar, V., Luc, D.T. Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators. Journal of Optimization Theory and Applications 101, 599–621 (1999). https://doi.org/10.1023/A:1021790120780
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DOI: https://doi.org/10.1023/A:1021790120780