Abstract:We show that assuming all the summand functions to be lower semicontinuous is not sufficient to ensure a (strong) fuzzy sum rule for subdifferentials in any infinite dimensional Banach space. From this we deduce that additional assumptions are also needed on functions for chain rules, multiplier rules for constrained minimization problems and Clarke-Ledyaev type mean value inequalities in the infinite dimensional setting.
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- Jon Vanderwerff
- Affiliation: Department of Mathematics, Walla Walla College, College Place, Washington 99324
- Email: email@example.com
- Qiji J. Zhu
- Affiliation: Department of Mathematics & Statistics, Western Michigan University, Kalamazoo, Michigan 49008
- Email: firstname.lastname@example.org
- Received by editor(s): January 30, 1997
- Additional Notes: The first author’s research was partially supported by a Walla Walla College Faculty Development Grant.
The second author’s work was partially supported by a grant from the Faculty Research and Creative Activities Support Fund, Western Michigan University.
Research for this note was completed while the authors were visiting Simon Fraser University. The authors thank J.M. Borwein and the CECM for their hospitality.
- Communicated by: Dale Alspach
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2691-2697
- MSC (1991): Primary 26B05, 49J50, 49J52
- DOI: https://doi.org/10.1090/S0002-9939-98-04365-2
- MathSciNet review: 1451834