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Mathematics > Optimization and Control

Title: Optimizing the Efficiency of First-order Methods for Decreasing the Gradient of Smooth Convex Functions

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 of the gradient norm. This work is based on the performance estimation problem approach. The corresponding worst-case gradient bound of the optimized method is optimal up to a constant for large-dimensional smooth convex minimization problems. This paper then illustrates that the resulting method, named OGM-G, has a computationally efficient form that is similar to the optimized gradient method (OGM).
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1803.06600 [math.OC]
  (or arXiv:1803.06600v1 [math.OC] for this version)

Submission history

From: Donghwan Kim [view email]
[v1] Sun, 18 Mar 2018 04:12:21 GMT (62kb)