Generic nondegeneracy in convex optimization
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- by Dmitriy Drusvyatskiy and Adrian S. Lewis PDF
- Proc. Amer. Math. Soc. 139 (2011), 2519-2527 Request permission
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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2519-2527
- MSC (2010): Primary 49J53, 32F32; Secondary 47H05
- DOI: https://doi.org/10.1090/S0002-9939-2010-10692-5
- MathSciNet review: 2784817