The dimension of semialgebraic subdifferential graphs

Details The dimension of semialgebraic subdifferential graphs The dimension of semialgebraic subdifferential graphs

2011-02-20

arxiv.org/abs/1102.4050v1

Mathematics

Optimization and Control

30 pages

Scientific paper

10.1016/j.na.2011.07.040.

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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