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arXiv · 1803.06600

Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions

Donghwan Kim·Jeffrey A. Fessler
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Abstract

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.

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Donghwan Kim, Jeffrey A. Fessler. 2018-03-18. Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions. https://arxiv.org/abs/1803.06600

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