Some regularity results for the pseudospectral abscissa and pseudospectral radius of a matrix

Mert Gürbüzbalaban; Michael L. Overton

doi:10.1137/110822840

Journal article, 2012

Some regularity results for the pseudospectral abscissa and pseudospectral radius of a matrix

Mert Gürbüzbalaban, Michael L. Overton

SIAM Journal on Optimization, 22(2), pp. 281–285, 2012.

Publisher (DOI)

In brief

The pseudospectral abscissa and radius measure the robust stability of a matrix, and optimizing them requires knowing how regular they are as functions of the matrix. The paper proves they are locally Lipschitz and, more strongly, regular in the sense of nonsmooth analysis near the relevant points, which is what the convergence theory of nonsmooth optimization methods needs.

Topics

Spectral & nonsmooth optimization

Cite

@article{gurbuzbalaban2012pseudospectral,
  title   = {Some regularity results for the pseudospectral abscissa and pseudospectral radius of a matrix},
  author  = {Mert Gürbüzbalaban and Michael L. Overton},
  year    = {2012},
  journal = {SIAM Journal on Optimization},
  volume  = {22(2)},
  pages   = {281--285},
  doi     = {10.1137/110822840},
}