Local Lipschitz-constant Functions and Maximal Subdifferentials |
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| Authors: | J M Borwein J Vanderwerff and Xianfu Wang |
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| Institution: | (1) Centre for Experimental and Constructive Mathematics, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;(2) Department of Mathematics and Computing, La Sierra University, Riverside, CA, 92515, U.S.A;(3) Department of Mathematics and Statistics, Okanagan University College, 3333 College Way, Kelowna, BC, V1V 1V7, Canada |
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| Abstract: | It is shown that if k(x) is an upper semicontinuous and quasi lower semicontinuous function on a Banach space X, then k(x)B
X* is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its  local Lipschitz-constant function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed. |
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| Keywords: | Lipschitz function Baire category Clarke subdifferential approximate subdifferential local Lipschitz-constant function |
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