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In this paper, we propose a fast proximal gradient algorithm formultiobjective optimization, it is proved that the convergence rate of theaccelerated algorithm for multiobjective optimization developed by Tanabe etal. can be improved from $O(1/k^2)$ to $o(1/k^2)$ by introducing differentextrapolation term $\frac{k-1}{k+\alpha-1}$ with $\alpha>3$. Further, weestablish the inexact version of the proposed algorithm when the error term isadditive, which owns the same convergence rate.  At last, the efficiency of the proposed algorithm is verified on somenumerical experiments.

The convergence rate of the accelerated proximal gradient algorithm for Multiobjective Optimization is faster than $O(1/k^2)$