The recent balanced augmented Lagrangian method (ALM) and its dual-primal version are effective for solving linearly constrained convex programming problems. We present accelerated (dual-primal) balanced ALM methods and establish \(\varvec{O(1/k^2)}\) (where \(\varvec{k}\) is the number of iterations) convergence rates in the case that the objective function to be minimized is strongly convex. Numerical results demonstrate the efficiency of the new accelerated algorithms.

中文翻译：

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$$O(1/k^2)$$线性约束凸规划的（双原始）平衡增强拉格朗日方法的收敛速度

最近的平衡增广拉格朗日方法（ALM）及其对偶原始版本对于解决线性约束凸规划问题非常有效。我们提出加速（双原始）平衡 ALM 方法并建立\(\varvec{O(1/k^2)}\)（其中\(\varvec{k}\)是迭代次数）要最小化的目标函数是强凸的情况。数值结果证明了新加速算法的效率。