On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization

Coralia Cartis, N.I.M. Gould, Philippe Toint

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Abstract

The (optimal) function/gradient evaluations worst-case complexity analysis available for the adaptive regularization algorithms with cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm, yielding complexity bounds for first-order and derivative-free methods applied on the same problem class. A comparison with the results obtained for derivative-free methods by Vicente [Worst Case Complexity of Direct Search, Technical report, Preprint 10-17, Department of Mathematics, University of Coimbra, Coimbra, Portugal, 2010] is also discussed, giving some theoretical insight into the relative merits of various methods in this popular class of algorithms. © 2012 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)66-86
Number of pages21
JournalSIAM Journal on Optimization
Volume22
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • nonconvex optimization.
  • finite-differences
  • oracle complexity
  • first-order methods
  • worst-case analysis
  • derivative free optimization

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