The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. Each block of the objective contains a further smooth convex function. We investigate the dynamical system proposed and prove that its trajectories asymptotically converge to a saddle point of the Lagrangian of the convex optimization problem. Time discretization of the dynamical system leads to the alternating minimization algorithm AMA and also to its proximal variant recently introduced in the literature.

中文翻译：

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具有线性约束的两块可分离凸优化问题的动力学方法

本手稿的目的是通过具有两块可分离线性约束和目标的一阶微分方程/包含凸规划问题来解决，其中（至少）后者的一个组件被假定为强凸的。目标的每个块都包含一个更平滑的凸函数。我们研究了所提出的动力系统，并证明其轨迹渐近收敛到凸优化问题的拉格朗日量的鞍点。动态系统的时间离散化导致交替最小化算法 AMA 及其最近在文献中引入的近端变体。