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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, 47H05 show english descriptions Applications in optimization, convex analysis, mathematical programming, economics
Monotone operators and generalizations
46N10 - Applications in optimization, convex analysis, mathematical programming, economics
47H05 - Monotone operators and generalizations
 

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