Abstract
We prove that the subdifferential of any semi-algebraic extended-real-valued function on \(\mathbf{R}^n\) has \(n\)-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.
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Acknowledgments
Thanks to Alex D. Ioffe for suggesting the extension we pursue in Sect. 5.
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D. Drusvyatskiy: Work of Dmitriy Drusvyatskiy on this paper has been partially supported by the NDSEG grant from the Department of Defense. A. S. Lewis: Research supported in part by National Science Foundation Grant DMS-0806057.
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Drusvyatskiy, D., Lewis, A.S. Semi-algebraic functions have small subdifferentials. Math. Program. 140, 5–29 (2013). https://doi.org/10.1007/s10107-012-0624-x
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DOI: https://doi.org/10.1007/s10107-012-0624-x