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On totally Fenchel unstable functions in finite dimensional spaces

Authors :
Andreas Löhne
Radu Ioan Boţ
Source :
Mathematical Programming. 123:25-31
Publication Year :
2009
Publisher :
Springer Science and Business Media LLC, 2009.

Abstract

We give an answer to the Problem 11.6 posed by Stephen Simons in his book “From Hahn-Banach to Monotonicity”: Do there exist a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally Fenchel unstable? The answer is negative.

Subjects

Subjects :
Mathematics::Functional Analysis
Pure mathematics
Fenchel's duality theorem
Function space
General Mathematics
Mathematical analysis
Banach space
Monotonic function
Cone (topology)
Recession cone
Convex optimization
Convex function
Software
Mathematics

Details

ISSN :
14364646 and 00255610
Volume :
123
Database :
OpenAIRE
Journal :
Mathematical Programming
Accession number :
edsair.doi...........f6d3d9a522c385525080e7f9281a6d88

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