Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 22, Issue 1, Pages 66-86Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100812276
Keywords
oracle complexity; worst-case analysis; finite differences; first-order methods; derivative-free optimization; nonconvex optimization
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Funding
- EPSRC [EP/E053351/1]
- Royal Society [14265]
- Engineering and Physical Sciences Research Council [EP/I013067/1, EP/E053351/1] Funding Source: researchfish
- EPSRC [EP/I013067/1, EP/E053351/1] Funding Source: UKRI
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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.
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