Polynomial root radius optimization with affine constraints

Julie Eaton; Sara Grundel; Mert Gürbüzbalaban; Michael L. Overton

doi:10.1007/s10107-016-1092-5

Journal article, 2017

Polynomial root radius optimization with affine constraints

Julie Eaton, Sara Grundel, Mert Gürbüzbalaban, Michael L. Overton

Mathematical Programming, 165(2), pp. 509–528, 2017.

Publisher (DOI)

In brief

Minimize the largest root modulus of a polynomial whose coefficients must satisfy a set of affine constraints — the problem behind stabilizing a discrete-time system with a controller of fixed structure. The optimal polynomial turns out to have very few distinct root moduli, which makes a non-convex, nonsmooth problem solvable in closed form in cases that matter for control.

Topics

Spectral & nonsmooth optimization

Cite

@article{eaton2017rootradius,
  title   = {Polynomial root radius optimization with affine constraints},
  author  = {Julie Eaton and Sara Grundel and Mert Gürbüzbalaban and Michael L. Overton},
  year    = {2017},
  journal = {Mathematical Programming},
  volume  = {165(2)},
  pages   = {509--528},
  doi     = {10.1007/s10107-016-1092-5},
}