论文标题
限制行为和增强作用在投影的马鞍流中进行凸优化
Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization
论文作者
论文摘要
在本文中，我们研究了连续时间拉格朗日马鞍流向凸的受约束优化问题的解决方案的稳定性和收敛性。当基础鞍函数严格凸出，或者在双重变量中严格凹入时，这些流的收敛性是众所周知的。在本文中，当添加简单的单方面增强项时，我们在非严格的凸度下显示融合。为此，我们建立了一种新颖的，非平凡的表征，对鞍 - 流轨迹的极限集，使我们能够阻止极限周期。在我们的演讲中，我们试图将几种现有的问题公式统一为一个投影的动力系统，允许对原始变量和双重变量进行投影，从而补充了最近文献中可用的结果。
In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is either strictly convex in the primal or strictly concave in the dual variables. In this paper, we show convergence under non-strict convexity when a simple, unilateral augmentation term is added. For this purpose, we establish a novel, non-trivial characterization of the limit set of saddle-flow trajectories that allows us to preclude limit cycles. With our presentation we try to unify several existing problem formulations as a projected dynamical system that allows projection of both the primal and dual variables, thus complementing results available in the recent literature.
