Application of Linearized Alternating Direction Multiplier Method in Dictionary Learning - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.1, January 2019

Journal of Applied Mathematics and Physics

Volume 7, Issue 1 (January 2019)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

Application of Linearized Alternating Direction Multiplier Method in Dictionary Learning ()

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Download as PDF (Size: 636KB) PP. 138-147

DOI: 10.4236/jamp.2019.71012 775 Downloads 1,599 Views Citations

Author(s)

Xiaoli Yu

Affiliation(s)

School of Science, School of Science and Technology, Shanghai University of Technology, Shanghai, China.

ABSTRACT

The Alternating Direction Multiplier Method (ADMM) is widely used in various fields, and different variables are customized in the literature for different application scenarios [1] [2] [3] [4]. Among them, the linearized alternating direction multiplier method (LADMM) has received extensive attention because of its effectiveness and ease of implementation. This paper mainly discusses the application of ADMM in dictionary learning (non-convex problem). Many numerical experiments show that to achieve higher convergence accuracy, the convergence speed of ADMM is slower, especially near the optimal solution. Therefore, we introduce the linearized alternating direction multiplier method (LADMM) to accelerate the convergence speed of ADMM. Specifically, the problem is solved by linearizing the quadratic term of the subproblem, and the convergence of the algorithm is proved. Finally, there is a brief summary of the full text.

KEYWORDS

Alternating Direction Multiplier Method, Dictionary Learning, Linearized Alternating Direction Multiplier, Non-Convex Optimization, Convergence

Share and Cite:

Yu, X. (2019) Application of Linearized Alternating Direction Multiplier Method in Dictionary Learning. Journal of Applied Mathematics and Physics, 7, 138-147. doi: 10.4236/jamp.2019.71012.

Cited by

[1]	A novel quasi-newton method for composite convex minimization
	Pattern Recognition, 2022

[2]	A linearized alternating direction method of multipliers for a special three-block nonconvex optimization problem of background/foreground extraction
	2020

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