By time discretization of a second-order primal–dual dynamical system with damping $\alpha /t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal–dual algorithm for a linear equality constrained convex optimization problem. Under a suitable scaling condition, we show that the proposed algorithm enjoys a fast convergence rate for the objective residual and the feasibility violation, and the decay rate can reach $\mathcal{O}(1/k^{\alpha -1})$ at the most. We also study convergence properties of the corresponding primal–dual dynamical system to better understand the acceleration scheme. Finally, we report numerical experiments to demonstrate the effectiveness of the proposed algorithm.

通过时间离散二阶原始-双动力系统的阻尼$\alpha /吨$在仅原始变量需要 Nesterov 意义上的惯性构造的情况下，我们提出了一种用于线性等式约束凸优化问题的快速原始对偶算法。在合适的尺度条件下，我们证明了该算法对目标残差和可行性违例具有较快的收敛速度，衰减率可以达到$\mathcal{○}(1/{ķ}^{\alpha -1})$至多，最多。我们还研究了相应的原始双动力系统的收敛特性，以更好地理解加速方案。最后，我们报告了数值实验来证明所提出算法的有效性。