On Nesterov's nonsmooth Chebyshev–Rosenbrock functions

Mert Gürbüzbalaban; Michael L. Overton

Journal article, 2012

On Nesterov's nonsmooth Chebyshev–Rosenbrock functions

Mert Gürbüzbalaban, Michael L. Overton

Nonlinear Analysis: Theory, Methods & Applications, 75(3), pp. 1282–1289, 2012. Invited paper, special issue on optimization.

Publisher page

In brief

Nesterov’s nonsmooth Chebyshev–Rosenbrock functions are a famous stress test for nonsmooth optimization methods. The paper explains why they are so hard: the first variant has exponentially many Clarke stationary points of which only one is a minimizer, so a method that converges to Clarke stationary points can stop almost anywhere, and the second variant is analyzed in the same spirit.

Topics

Spectral & nonsmooth optimization

Cite

@article{gurbuzbalaban2012nesterov,
  title   = {On Nesterov's nonsmooth Chebyshev–Rosenbrock functions},
  author  = {Mert Gürbüzbalaban and Michael L. Overton},
  year    = {2012},
  journal = {Nonlinear Analysis: Theory, Methods & Applications},
  volume  = {75(3)},
  pages   = {1282--1289},
  url     = {https://www.sciencedirect.com/science/article/pii/S0362546X1100544X},
}