On the subdifferential regularity of max root functions for polynomials. (English) Zbl 1236.49078
Summary: In 2001, J. L. Burke and M. L. Overton [”Variational analysis of the abscissa mapping for polynomials”, SIAM J. Control Optimization 39, No.6, 1651-1676 (2001, Zbl 0997.49015)]
showed that the abscissa mapping on polynomials is subdifferentially regular on the monic polynomials of degree \(n\). We extend this result to the class of max polynomial root functions which includes both the polynomial abscissa and the polynomial radius mappings. The approach to the computation of the subgradient simplifies that given by Burke and Overton and provides new insight into the variational properties of these functions.
Keywords:
spectral radius; spectral abscissa; polynomial root functions; subdifferential regularity; max polynomial root functionsCitations:
Zbl 0997.49015References:
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