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arXiv · 1102.4050

The dimension of semialgebraic subdifferential graphs

Dmitriy Drusvyatskiy·Alexander D. Ioffe·Adrian S. Lewis
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Abstract

Examples exist of extended-real-valued closed functions on ${\bf R}^n$ 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.

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Dmitriy Drusvyatskiy, Alexander D. Ioffe, Adrian S. Lewis. 2011-02-20. The dimension of semialgebraic subdifferential graphs. https://doi.org/10.1016/j.na.2011.07.040.

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