The Equivalence of Several Basic Theorems for Subdifferentials |
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Authors: | Qiji J. Zhu |
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Affiliation: | (1) Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI, 49008, U.S.A. |
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Abstract: | Several different basic tools are used for studying subdifferentials. They are a nonlocal fuzzy sum rule in (Borwein et al., 1996; Zhu, 1996), a multidirectional mean value theorem in (Clarke and Ledyaev, 1994; Clarke et al., 1998), local fuzzy sum rules in (Ioffe, 1984, 1990) and an extremal principle in (Kruger and Mordukhovich, 1980; Mordukhovich, 1976, 1980, 1994). We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence. |
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Keywords: | subdifferentials mean value inequalities local fuzzy sum rules nonlocal fuzzy sum rules extremal principles and Asplund spaces |
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