Relaxed Variable Metric Primal-Dual Fixed-Point Algorithm with Applications

In this paper, a relaxed variable metric primal-dual fixed-point algorithm is proposed for solving the convex optimization problem involving sum of two functions where one differentiable with Lipschitz continuous gradient while other composed linear operator. Based on preconditioned forward–backward splitting algorithm, convergence proved. At same time, we show that some existing algorithms are special cases algorithm. Furthermore, ergodic and rates established under parameters. Numerical experiments image deblurring problems demonstrate outperforms in terms number iterations.