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

Donghwan Kim () and Jeffrey A. Fessler ()
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Donghwan Kim: Korea Advanced Institute of Science and Technology (KAIST)
Jeffrey A. Fessler: University of Michigan

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 1, No 9, 192-219

Abstract: 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.

Keywords: First-order methods; Gradient methods; Smooth convex minimization; Worst-case performance analysis; 90C25; 90C30; 90C60; 68Q25; 49M25; 90C22 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-020-01770-2

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