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The dimension of semialgebraic subdifferential graphs.

Dmitriy Drusvyatskiy(dd379***at***cornell.edu)
Alexander D. Ioffe(ioffe***at***math.technion.ac.il)
Adrian S. Lewis(aslewis***at***orie.cornell.edu )

Abstract: Examples exist of extended-real-valued closed functions on $\R^n$ whose subdifferentials (in the standard, limiting sense) have large graphs. By contrast, if such a function is semi-algebraic, then its subdifferential graph must have everywhere constant local dimension $n$. This result is related to a celebrated theorem of Minty, and surprisingly may fail for the Clarke subdifferential.

Keywords: Set-valued map, subdifferential, semi-algebraic, stratification, dimension.

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.

Download: [PDF]

Entry Submitted: 02/18/2011
Entry Accepted: 02/18/2011
Entry Last Modified: 02/18/2011

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