论文标题
凸入岩体鞍点问题的梯度下降方法的收敛率分析
Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems
论文作者
论文摘要
在本文中，我们研究了用于凸入concave鞍点问题的梯度下降方法。我们通过使用半决赛编程性能估计方法来得出一个新的非质合全局收敛速率，以与解决方案设置的距离。给定的收敛速率包含了问题的大多数参数，对于一大批强烈凸出的凹入的鞍点问题是一个迭代的大量参数。我们还没有强大的凸度调查算法，并提供了一些必要和充分的条件，在这些条件下，梯度下降呈线性收敛。
In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming performance estimation method. The given convergence rate incorporates most parameters of the problem and it is exact for a large class of strongly convex-strongly concave saddle-point problems for one iteration. We also investigate the algorithm without strong convexity and we provide some necessary and sufficient conditions under which the gradient descent-ascent enjoys linear convergence.
