论文标题
通过线性约束的两块可分离凸优化问题的动态方法
A Dynamical Approach to Two-Block Separable Convex Optimization Problems with Linear Constraints
论文作者
论文摘要
本手稿的目的是通过一阶微分方程/包含物来实现，凸出编程问题，具有两个可分离的线性约束和目标，该问题（至少）将后者的一个组件之一（至少）被认为是强烈凸的。物镜的每个块都包含一个进一步的平滑凸函数。我们研究了提出的动力学系统，并证明其轨迹渐近地收敛到凸优化问题的拉格朗日的鞍点。动态系统的时间离散化导致交替的最小化算法AMA以及最近在文献中引入的近端变体。
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.
