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 | References | Similar Articles | Additional Information

Abstract: We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally for *lower- * 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:
https://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.