Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators

V. Jeyakumar and D. T. Luc
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V. Jeyakumar: University of New South Wales
D. T. Luc: Institute of Mathematics

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 3, No 5, 599-621

Abstract: 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.

Keywords: Upper convex approximations; lower concave approximations; nonsmooth analysis; extremality; mean-value conditions; quasiconvexity; quasimonotonicity (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (22)

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DOI: 10.1023/A:1021790120780

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