Explicit solutions for root optimization of a polynomial family with one affine constraint

Vincent D. Blondel; Mert Gürbüzbalaban; Alexandre Megretski; Michael L. Overton

doi:10.1109/TAC.2012.2202069

Journal article, 2012

Explicit solutions for root optimization of a polynomial family with one affine constraint

Vincent D. Blondel, Mert Gürbüzbalaban, Alexandre Megretski, Michael L. Overton

IEEE Transactions on Automatic Control, 57(12), pp. 3078–3089, 2012.

Publisher (DOI)

In brief

Among all monic polynomials whose coefficients satisfy a single affine constraint, which one has the smallest root radius, or the smallest root abscissa? The answer is explicit: the optimal polynomial has all of its roots at one point, and the paper gives that point, which settles the simplest version of the fixed-order stabilization problem in control.

Topics

Spectral & nonsmooth optimization

Cite

@article{blondel2012root,
  title   = {Explicit solutions for root optimization of a polynomial family with one affine constraint},
  author  = {Vincent D. Blondel and Mert Gürbüzbalaban and Alexandre Megretski and Michael L. Overton},
  year    = {2012},
  journal = {IEEE Transactions on Automatic Control},
  volume  = {57(12)},
  pages   = {3078--3089},
  doi     = {10.1109/TAC.2012.2202069},
}