Note 1: This article is one of the "Concept Analysis" series, which is dedicated to explaining and distinguishing complex and professional concepts concisely and clearly. The concept of this analysis is: Alternating Direction Method of Multipliers (ADMM).
Decoding ADMM: Principles, Applications and Prospects of the Alternating Direction Multiplier Method
1. Background introduction
In optimization problems, especially when dealing with large-scale and distributed optimization problems, Alternating Direction Method of Multipliers (ADMM for short) is a very effective method. Its main advantage is that it can decompose a complex optimization problem into a series of more tractable subproblems. ADMM methods are widely used in signal processing, machine learning, statistics and other fields.
2. Principle introduction and derivation
ADMM is based on the combination of Augmented Lagrangian method (augmented Lagrangian method) and dual ascent (dual rising method). Its goal is to solve problems of the form:
min