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# Subdifferentials Whose Graphs Are Not Norm$\times$Weak* Closed

Published:2003-12-01
Printed: Dec 2003
• Jonathan Borwein
• Simon Fitzpatrick
• Roland Girgensohn
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## Abstract

In this note we give examples of convex functions whose subdifferentials have unpleasant properties. Particularly, we exhibit a proper lower semicontinuous convex function on a separable Hilbert space such that the graph of its subdifferential is not closed in the product of the norm and bounded weak topologies. We also exhibit a set whose sequential normal cone is not norm closed.
 MSC Classifications: 46N10 - Applications in optimization, convex analysis, mathematical programming, economics 47H05 - Monotone operators and generalizations

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