Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 14, Issue 4, Pages 1043-1056Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1052623403428208
Keywords
nonmonotone line search; R-linear convergence; unconstrained optimization; L-BFGS method
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A new nonmonotone line search algorithm is proposed and analyzed. In our scheme, we require that an average of the successive function values decreases, while the traditional nonmonotone approach of Grippo, Lampariello, and Lucidi [SIAM J. Numer. Anal., 23 ( 1986), pp. 707 - 716] requires that a maximum of recent function values decreases. We prove global convergence for nonconvex, smooth functions, and R-linear convergence for strongly convex functions. For the L-BFGS method and the unconstrained optimization problems in the CUTE library, the new nonmonotone line search algorithm used fewer function and gradient evaluations, on average, than either the monotone or the traditional nonmonotone scheme.
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