Semi-algebraic functions have small subdifferentials

2010/04/02 by Drusvyatskiy, Dmitriy, Lewis, Adrian S. · 1 citation
#14P10 (primary) 54C60 #49J53 #57N80 #58C07 (secondary) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1004.0368

Abstract

We prove that the subdifferential of any semi-algebraic extended-real-valued function on \Rⁿ has n-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.

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