Nesterov's Accelerating Technique for Composite Optimization

讲座内容：In many applied areas such as compressed sensing and machine learning, it is commonly needed to solve a composite optimization problem where the objective function is a sum of two (or more) component functions, one of which may have a simple structure and plays the role of regularization. To solve such a composite optimization problem, the proximal algorithm is prevailingly applied. This algorithm has however a slow sublinear rate of convergence. Yu. Nesterov (1983) initiated an acceleration method which can speed up the convergence rate of the gradient-projection algorithm from O(1/k) to O(1/k^2). This is extended to the case of composite optimization by Beck and Teboulle in 2009. Since then Nesterov's acceleration has been paid a lot of attention by researchers from various areas including optimization, engineering, computer science, statistics, and so on. In this talk, we will briey introduce the results on the study of Nesterov's accel- eration technique and its application in big data problems and connection with the asymptotics of certain dynamic systems.