Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators |
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| Authors: | V Jeyakumar D T Luc |
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| Institution: | (1) Department of Applied Mathematics, University of New South Wales, Sydney, Australia;(2) Institute of Mathematics, Hanoi, Vietnam |
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| 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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| Keywords: | Upper convex approximations lower concave approximations nonsmooth analysis extremality mean-value conditions quasiconvexity quasimonotonicity |
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