Solving Large-scale Optimization Problems using Proximal Methods
As we move towards the realm of Big Data, traditional optimization algorithms that rely on batch computation and sequential updates are faced with fundamental difficulties. Recently, a new generation of optimization tools called proximal methods is gaining ground. Generally, a proximal algorithm factorizes a large problem into a number of sub-problems -- each can be solved efficiently by evaluating a proximal operator. These methods are particularly suited for problems involving large-scale datasets and distributed environments. In this talk, I will introduce the basics of proximal methods, extend their applications to distributed problems via consensus, and discuss several issues that remain open.