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.
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