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Wang, Y.L., Yang, J.F., Yin, W.T., et al. (2016) A New Alternating Minimization Algorithm for Total Variation Image Reconstruction. SIAM Journal on Imaging Sciences, 1, 248–272.

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• TITLE: Application of Linearized Alternating Direction Multiplier Method in Dictionary Learning

  AUTHORS: Xiaoli Yu

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.1, January 18, 2019

  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.