Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems
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Authors
Hongchun Sun
- School of Sciences, Linyi University, Shandong 276005, P. R. China.
Min Sun
- School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, P. R. China.
- School of Management, Qufu Normal University, Shandong 276826, P. R. China.
Yiju Wang
- School of Management, Qufu Normal University, Shandong 276826, P. R. China.
Abstract
The alternating direction method of multipliers (ADMM) is a benchmark for solving two-block separable convex programming. However, as other first-order iteration methods, the ADMM also suffers from low convergence. In this paper, to accelerate the convergence of {the} ADMM, the restriction region of the Fortin and Glowinski's constant \(\gamma\) in the ADMM is relaxed from \(\Big(0,\frac{1+\sqrt{5}}{2}\Big)\) to \((0,+\infty)\), thus we get a proximal ADMM with larger step size. By proving some properties of the method, we show its global
convergence under mild conditions. Finally, some numerical experiments on the correlation matrices calibrating problems are given to demonstrate the efficiency and the performance of the new method.
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ISRP Style
Hongchun Sun, Min Sun, Yiju Wang, Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 5038--5051
AMA Style
Sun Hongchun, Sun Min, Wang Yiju, Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems. J. Nonlinear Sci. Appl. (2017); 10(9):5038--5051
Chicago/Turabian Style
Sun, Hongchun, Sun, Min, Wang, Yiju. "Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 5038--5051
Keywords
- Alternating direction method of multipliers
- the Fortin and Glowinski's constant
- global convergence
MSC
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