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Semi-algebraic functions have small subdifferentials

Dmitriy Drusvyatskiy (dd379***at***cornell.edu)
Adrian S. Lewis (aslewis***at***orie.cornell.edu)

Abstract: We prove that the subdifferential of any semi-algebraic extended-real-valued function on $\R^n$ has $n$-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.

Keywords: semi-algebraic, subdifferential, critical, nondegeneracy

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Cornell University, School of Operations Research and Information Engineering, 206 Rhodes Hall Cornell University Ithaca, NY 14853. April 2010.

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Entry Submitted: 04/02/2010
Entry Accepted: 04/02/2010
Entry Last Modified: 04/02/2010

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