Porosity of ill-posed problems

Authors:
Robert Deville and Julian P. Revalski

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1117-1124

MSC (1991):
Primary 46B20, 49J45

DOI:
https://doi.org/10.1090/S0002-9939-99-05091-1

Published electronically:
August 5, 1999

MathSciNet review:
1636942

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that in several classes of optimization problems, including the setting of smooth variational principles, the complement of the set of well-posed problems is -porous.

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Additional Information

**Robert Deville**

Affiliation:
Laboratoire de Mathématiques, Université de Bordeaux, 351, cours de la Libération, 33 400 Talence, France

Email:
deville@math.u-bordeaux.fr

**Julian P. Revalski**

Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, block 8, 1113 Sofia, Bulgaria

DOI:
https://doi.org/10.1090/S0002-9939-99-05091-1

Keywords:
Variational principles,
well-posed optimization problems,
ill-posed problems,
porous sets,
porosity

Received by editor(s):
March 24, 1998

Received by editor(s) in revised form:
June 1, 1998

Published electronically:
August 5, 1999

Additional Notes:
This paper was initiated during a short visit of the second named author in November 1997, in the University of Bordeaux

The second author was partially supported by the Bulgarian National Fund for Scientific Research under contract No. MM-701/97

Communicated by:
Dale Alspach

Article copyright:
© Copyright 2000
American Mathematical Society