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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Generic nondegeneracy in convex optimization


Authors: Dmitriy Drusvyatskiy and Adrian S. Lewis
Journal: Proc. Amer. Math. Soc. 139 (2011), 2519-2527
MSC (2010): Primary 49J53, 32F32; Secondary 47H05
Published electronically: December 21, 2010
MathSciNet review: 2784817
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Abstract: We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally for lower- $ \mathbf{C}^2$ functions.


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Additional Information

Dmitriy Drusvyatskiy
Affiliation: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
Email: dd379@cornell.edu

Adrian S. Lewis
Affiliation: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10692-5
Keywords: Convex functions, normal cone, subdifferential, Hausdorff measure, lower-$\mathbf{C}^{2}$ functions
Received by editor(s): May 5, 2010
Received by editor(s) in revised form: July 8, 2010
Published electronically: December 21, 2010
Additional Notes: The work of the first author was supported in part by the NDSEG grant from the Department of Defense.
The work of the second author was supported in part by National Science Foundation Grant DMS-0806057.
Communicated by: Tatiana Toro
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.