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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
Published electronically: August 5, 1999
MathSciNet review: 1636942
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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 $\sigma$-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

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

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