A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function

Coralia Cartis, Nicholas I M Gould, Philippe L. Toint

Research output: Contribution to journalArticlepeer-review

72 Downloads (Pure)

Abstract

This short note considers and resolves the apparent contradiction between known worst-case complexity results for first- and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre [On Nesterov's smooth Chebyshev-Rosenbrock function, Optim. Methods Softw. (2011)] implying a very large lower bound on the number of iterations required to reach the solution's neighbourhood for a specific problem with variable dimension.

Original languageEnglish
Pages (from-to)451-457
Number of pages7
JournalOptimization Methods and Software
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Jun 2013

Keywords

  • evaluation complexity
  • nonconvex optimization
  • worst-case analysis

Fingerprint Dive into the research topics of 'A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function'. Together they form a unique fingerprint.

Cite this