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Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration

Speaker

Jingwei Liang, University of Cambridge

Time

2020.01.09 10:30-11:30

Venue

Room 306, No.5 Science Building

Abstract

The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to improve the performance of the method, such as the inertial technique. In this talk, I will first discuss the limitation of inertial technique when applied to ADMM. Motivated by the failure of inertial ADMM, a framework on studying the geometric property of ADMM is provided which focuses on the trajectory of the generated sequence. Consequently, an adaptive acceleration scheme for ADMM is proposed based on the trajectory. Numerical experiments on problems arising from image processing, statistics and machine learning demonstrate the advantages of the proposed acceleration approach.