Journal
MATHEMATICAL PROGRAMMING
Volume 190, Issue 1-2, Pages 57-87Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-021-01643-0
Keywords
Proximal point method; Acceleration; Maximally monotone operators; Worst-case performance analysis
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Funding
- National Research Foundation of Korea (NRF) - Korea Government (MSIT) [2019R1A5A1028324]
- POSCO Science Fellowship of POSCO TJ Park Foundation
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This paper introduces an accelerated proximal point method for maximally monotone operators, with computer-assisted proof using the performance estimation problem approach. By incorporating various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers, the proposed acceleration technique has wide applications. Numerical experiments demonstrate the accelerating behavior of the method.
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers, and thus the proposed acceleration has wide applications. Numerical experiments are presented to demonstrate the accelerating behaviors.
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