This paper considers convex programs with a general (possibly
non-differentiable) convex objective function and Lipschitz continuous convex
inequality constraint functions. A simple algorithm is developed and achieves
an $O(1/t)$ convergence rate. Similar to the classical dual subgradient
algorithm and the ADMM algorithm, the new algorithm has a parallel
implementation when the objective and constraint functions are separable.
However, the new algorithm has a faster $O(1/t)$ convergence rate compared with
the best known $O(1/\sqrt{t})$ convergence rate for the dual subgradient
algorithm with primal averaging. Further, it can solve convex programs with
nonlinear constraints, which cannot be handled by the ADMM algorithm. The new
algorithm is applied to a multipath network utility maximization problem and
yields a decentralized flow control algorithm with the fast $O(1/t)$
convergence rate.

本文研究具有一般凸目标函数和 Lipschitz 连续凸不等式约束函数的凸规划问题，并提出了一种简单的算法，用于实现 O (1/t) 的收敛速度。此外，该算法还可用于处理非线性约束条件。最终将该算法应用于多路径网络效用最大化问题，并产生具有快速 O (1/t) 收敛速度的分散式流量控制算法。