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Journal of Convex Analysis, Vol. 5, No. 2, pp. 221-235 (1998)
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Limiting Convex Examples for Nonconvex Subdifferential Calculus

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Jonathan M. Borwein and Qiji J. Zhu

CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, B. C. V5A 1S6, Canada, jborwein@cecm.sfu.ca, and Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA, zhu@math-stat.wmich.edu

**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

**Full text of the article:**

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