Journal of Convex Analysis, Vol. 5, No. 2, pp. 221-235 (1998)

Limiting Convex Examples for Nonconvex Subdifferential Calculus

Jonathan M. Borwein and Qiji J. Zhu

CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, B. C. V5A 1S6, Canada,, and Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA,

Abstract: We show, largely using convex examples, that most of the core results for limiting subdifferential calculus fail without additional restrictions in infinite dimensional Banach spaces.

Keywords: Nonsmooth analysis, subdifferentials, coderivatives, extremal principle, open mapping theorem, metric regularity, multiplier rules, compactly Lipschitzian conditions

Classification (MSC2000): 26B05

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