A fundamental proof of inexact accelerated proximal point algorithm for solving the maximal monotone inclusion problem

We propose an inexact accelerated proximal point algorithm for solving the maximal monotone inclusion problem. By a fundamental proof, a convergence rate of O(1/k) for the fixed-point residual is established under a novel inexact criterion for subproblem solutions, where k denotes the iteration index. Additionally, numerical experiments are conducted to validate the theoretical findings, demonstrating that the proposed algorithm is efficient.