Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

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 $\sigma$-porous.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46B20, 49J45

Retrieve articles in all journals with MSC (1991): 46B20, 49J45


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: http://dx.doi.org/10.1090/S0002-9939-99-05091-1
PII: S 0002-9939(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