Dual representation of monotone convex functions on

Authors:
Michael Kupper and Gregor Svindland

Journal:
Proc. Amer. Math. Soc. **139** (2011), 4073-4086

MSC (2010):
Primary 46A16, 46A20, 49N15, 91G99

DOI:
https://doi.org/10.1090/S0002-9939-2011-10835-9

Published electronically:
April 12, 2011

MathSciNet review:
2823052

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study monotone convex functions and derive a dual representation as well as conditions that ensure the existence of a -additive subgradient. The results are motivated by applications in economic agents' choice theory.

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Additional Information

**Michael Kupper**

Affiliation:
Mathematics Institute, Humboldt University Berlin, Unter den Linden 6, D-10099 Berlin, Germany

Email:
kupper@math.hu-berlin.de

**Gregor Svindland**

Affiliation:
École Polytechnique Fédérale de Lausanne, CDM SFI CSF - EXTRA 218, CH-1015 Lausanne, Switzerland

Address at time of publication:
Department of Mathematics, University of Munich, Theresienstr. 39, D-80333 Munich, Germany

Email:
gregor.svindland@epfl.ch, svindla@math.lmu.de

DOI:
https://doi.org/10.1090/S0002-9939-2011-10835-9

Keywords:
Monotone convex function,
duality,
subgradient,
bipolar representation

Received by editor(s):
April 22, 2010

Received by editor(s) in revised form:
October 7, 2010

Published electronically:
April 12, 2011

Additional Notes:
The first author gratefully acknowledges financial support from the MATHEON project E.11

The second author gratefully acknowledges support from Swissquote

Communicated by:
Richard Rochberg

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.