Rate of Convergence of the Bundle Method

Yu Du; Andrzej Ruszczynski

Rate of Convergence of the Bundle Method

Optimization and Control 2016-09-06 v1

Authors: Yu Du , Andrzej Ruszczynski

Abstract

We prove that the bundle method for nonsmooth optimization achieves solution accuracy $\varepsilon$ in at most $\mathcal{O}\big(\ln(1/\varepsilon)/\varepsilon\big)$ iterations, if the function is strongly convex. The result is true for the versions of the method with multiple cuts and with cut aggregation.

Keywords

bundle method nonsmooth optimization rate of convergence strongly convex cut aggregation

Cite

@article{arxiv.1609.00842,
  title  = {Rate of Convergence of the Bundle Method},
  author = {Yu Du and Andrzej Ruszczynski},
  journal= {arXiv preprint arXiv:1609.00842},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1511.01716

Related papers

View all related →