A nonmonotone line search technique and its application to unconstrained optimization
A nonmonotone line search technique and its application to unconstrained optimization
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DOI：
10.1137/s1052623403428208
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发表时间：
2004-01-01
影响因子：
3.1
通讯作者：
Hager, WW
中科院分区：
文献类型：
--
作者：
Zhang, HC;Hager, WW
提出并分析了一种新的非单调线搜索算法。在我们的方案中，我们要求连续函数值的平均值递减，而传统的Grippo，Lampariello和Lucidi的非单调方法[SIAM J. Numer.分析：23（1986），pp. 707 - 716]要求最近函数值的最大值减小。证明了非凸光滑函数的全局收敛性和强凸函数的R-线性收敛性。对于L-BFGS方法和CUTE库中的无约束优化问题，新的非单调线搜索算法比单调和传统的非单调算法平均使用更少的函数和梯度计算。
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.