The Equivalence of Several Basic Theorems for Subdifferentials
- Qiji J. Zhu
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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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- The Equivalence of Several Basic Theorems for Subdifferentials
Volume 6, Issue 2 , pp 171-185
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- mean value inequalities
- local fuzzy sum rules
- nonlocal fuzzy sum rules
- extremal principles and Asplund spaces
- Qiji J. Zhu (1)
- Author Affiliations
- 1. Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI, 49008, U.S.A.