Accelerated primal dual fixed point algorithm

Abstract: This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features fully decoupled iterations and can be regarded as a generalization of Nesterov's accelerated gradient in the setting where B can be a non-identity matrix. Theoretically, we improve the convergence rate of the partial primal-dual gap with respect to the Lipschitz constant of the gradient of f from O(1/k) to O(1/k^2). Numerical experiments on graph-guided logistic regression and CT image reconstruction are conducted to validate the correctness and demonstrate the efficiency of the proposed method.