Extremal points of a functional

on the set of convex functions

Authors:
T. Lachand-Robert and M. A. Peletier

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1723-1727

MSC (1991):
Primary 49K99

Published electronically:
February 11, 1999

MathSciNet review:
1646197

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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the extremal points of a functional , for a convex or concave function . The admissible functions are convex themselves and satisfy a condition . We show that the extremal points are exactly and if these functions are convex and coincide on the boundary . No explicit regularity condition is imposed on , , or . Subsequently we discuss a number of extensions, such as the case when or are non-convex or do not coincide on the boundary, when the function also depends on , etc.

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Additional Information

**T. Lachand-Robert**

Affiliation:
Université Pierre et Marie Curie, Laboratoire d’Analyse Numérique, 75252 Paris Cedex 05, France

Email:
lachand@ann.jussieu.fr

**M. A. Peletier**

Affiliation:
University of Bath, Claverton Down, Bath BA2 7AY United Kingdom

Email:
M.A.Peletier@bath.ac.uk

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05209-0

Keywords:
Extremal points,
convexity constraint,
non-convex minimization

Received by editor(s):
September 10, 1997

Published electronically:
February 11, 1999

Additional Notes:
Part of this work was carried out during a visit of the second author to Université Pierre et Marie Curie under the contract of the European Union 921 CHRX CT 94.

Communicated by:
Jeffrey B. Rauch

Article copyright:
© Copyright 1999
American Mathematical Society