This work proposes an Accelerated Primal–Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form $$\min_x\, f(x)+g\circ B(x)$$, 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 the setting where the $$B$$ can be non identity matrix.Theoretically, we improve the convergence rate of the partial primal-dual gap with respect to the Lipschitz constant of gradient of $$f$$ from $$\mathcal{O}(\frac{1}{k})$$ to $$\mathcal{O}(\frac{1}{k^2})$$. 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.
