Primaldual algorithms for the sum of two and three functions

Speaker: Ming Yan(Michigan State University)

Time: Dec 13, 2017, 16:0017:00
There are several primaldual algorithms for minimizing f(x)+g(x)+h(Ax), where f, g, and h are convex functions, f is differentiable with a Lipschitz continuous gradient, and A is a bounded linear operator. Two examples for minimizing the sum of two functions are ChambollePock (f=0) and Proximal Alternating PredictorCorrector (PAPC) (g=0). In this talk, I will introduce a new primaldual algorithm for minimizing the sum of three functions. This new algorithm has the ChambollePock and PAPC as special cases. It also enjoys most advantages of existing algorithms for solving the same problem. In addition, I will show that the parameters for PAPC can be relaxed. Then I will give some applications in decentralized consensus optimization.