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.

中文翻译：

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优化降低平滑凸函数梯度的一阶方法的效率

本文根据梯度范数减少的最坏情况收敛边界（即效率）优化平滑凸最小化的一阶方法的步长系数。这项工作基于性能估计问题方法。在成本函数值的初始有界条件下，对于大维平滑凸最小化问题，所得方法的最坏情况梯度边界是最优的，最多为常数。然后，本文说明了所提出的方法具有类似于优化梯度方法的计算效率形式。