Gradient Methods for Nonstationary Unconstrained Optimization Problems
Gradient Methods for Nonstationary Unconstrained Optimization Problems
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DOI：
10.1007/s10513-005-0132-z
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发表时间：
2005-06
影响因子：
0.7
通讯作者：
A. Popkov
中科院分区：
文献类型：
--
作者：
A. Popkov
考虑目标函数依赖于标量参数（时间）的无约束优化问题。这些问题的解也依赖于时间，任何数值方法都必须跟踪这种依赖关系。对于这类非定常问题的求解，本文提出了一种离散梯度法，该方法对每一时刻的变函数只取一个梯度步长。精确解和近似解之间的区间（变化）的估计被发现，并定义了这些估计的渐近行为。
Problems of unconstrained optimization with an objective function depending on a scalar parameter (time) are considered. The solution of these problems also depends on time and any numerical method must keep track of this dependence. For the solution of such nonstationary problems, a discrete gradient method is treated, in which only one gradient step is taken for the varying function at each instant of time. Estimates of intervals (variations) between exact and approximate solutions are found and an asymptotic behavior of these estimates is defined.