Computational & Applied Math Seminar

There are several primal-dual 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 Chambolle-Pock (f=0) and Proximal Alternating Predictor-Corrector (PAPC) (g=0). In this talk, I will introduce a new primal-dual algorithm for minimizing the sum of three functions. This new algorithm has the Chambolle-Pock 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.