The dimension of semialgebraic subdifferential graphs.
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.
Entry Submitted: 02/18/2011
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