论文标题
在随着时间变化的网络上，用于分散的优化问题的梯度型方法
Gradient-Type Methods For Decentralized Optimization Problems With Polyak-Łojasiewicz Condition Over Time-Varying Networks
论文作者
论文摘要
本文着重于满足Polyak-lojasiewicz条件（PL条件）的目标函数的分散优化（最小化和鞍点）问题。本文的第一部分致力于总体成本函数的最小化问题。为了解决此类问题，我们提出了一种具有共识投影过程和目标不精确梯度的梯度下降类型方法。接下来，在第二部分中，我们以总和的结构来研究鞍点问题（SPP），并具有满足双面PL条件的目标。为了解决此类SPP，我们提出了具有共识过程的多步梯度下降方法的概括，以及相对于两个变量的目标函数的不精确梯度。最后，我们提出了一些数值实验，以显示出可靠的最小二乘问题所提出的算法的效率。
This paper focuses on the decentralized optimization (minimization and saddle point) problems with objective functions that satisfy Polyak-Łojasiewicz condition (PL-condition). The first part of the paper is devoted to the minimization problem of the sum-type cost functions. In order to solve a such class of problems, we propose a gradient descent type method with a consensus projection procedure and the inexact gradient of the objectives. Next, in the second part, we study the saddle-point problem (SPP) with a structure of the sum, with objectives satisfying the two-sided PL-condition. To solve such SPP, we propose a generalization of the Multi-step Gradient Descent Ascent method with a consensus procedure, and inexact gradients of the objective function with respect to both variables. Finally, we present some of the numerical experiments, to show the efficiency of the proposed algorithm for the robust least squares problem.
