Motivated by the recent work [He-Yuan, Balanced Augmented Lagrangian Method for Convex Programming, arXiv: 2108.08554v1, (2021)], a novel Augmented Lagrangian Method (ALM) has been proposed for solving a family of convex optimization problem subject to equality or inequality constraint. This new method is then extended to solve the multi-block separable convex optimization problem, and two related primal-dual hybrid gradient algorithms are also discussed. Preliminary and some new convergence results are established with the aid of variational analysis for both the saddle point of the problem and the first-order optimality conditions of involved subproblems.

翻译：以最近的工作为动因[He-Yuan,平衡增强拉格朗加法的 Convex 编程方法, ArXiv: 21080.88554v1, (2021)],提出了一种新的拉格朗加法(ALM),旨在解决受平等或不平等制约的 convex优化问题大家庭,然后将这一新方法扩大到解决多块可分解的 convex 优化问题,并讨论了两个相关的原始-双重混合梯度算法。在对问题的顶点和所涉子问题的第一阶最佳条件进行变式分析的辅助下,初步和一些新的趋同结果得以确立。