论文标题
具有非平滑目标函数的部分原始双侧梯度动力学的指数稳定性
Exponential Stability of Partial Primal-Dual Gradient Dynamics with Nonsmooth Objective Functions
论文作者
论文摘要
在本文中，我们调查了连续时间部分的偶尔二梯度动力学（p-pdgd），用于求解凸的优化问题，其形式$ \ min \ limits_ {x \ in x，y \inΩ} \ f（{x}} {x}）+h（y）+h（y）+h（y）强烈凸出且光滑，但是$ h（y）$是强烈的凸面和非平滑的。包括仿射平等和集合约束。我们证明了P-PDGD的指数稳定性，并提供了衰减率的界限。此外，还表明可以通过设置步骤大小来调节衰减率。
In this paper, we investigate the continuous time partial primal-dual gradient dynamics (P-PDGD) for solving convex optimization problems with the form $ \min\limits_{x\in X,y\inΩ}\ f({x})+h(y),\ \textit{s.t.}\ A{x}+By=C $, where $ f({x}) $ is strongly convex and smooth, but $ h(y) $ is strongly convex and non-smooth. Affine equality and set constraints are included. We prove the exponential stability of P-PDGD, and bounds on decaying rates are provided. Moreover, it is also shown that the decaying rates can be regulated by setting the stepsize.
