Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions
Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions
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DOI：
10.1007/s10957-020-01770-2
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发表时间：
2018-03
影响因子：
1.9
通讯作者：
Donghwan Kim;J. Fessler
中科院分区：
文献类型：
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作者：
Donghwan Kim;J. Fessler
本文根据梯度范数减小的最坏情况收敛界（即效率），对光滑凸最小化一阶方法的阶跃系数进行了优化。这项工作是基于性能估计问题的方法。对于大维光滑凸最小化问题，在代价函数值的初始有界条件下，所得方法的最坏情况梯度界最优到一个常数。然后，本文说明了该方法具有类似于优化梯度法的计算效率形式。
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance estimation problem approach. The worst-case gradient bound of the resulting method is optimal up to a constant for large-dimensional smooth convex minimization problems, under the initial bounded condition on the cost function value. This paper then illustrates that the proposed method has a computationally efficient form that is similar to the optimized gradient method.