论文标题
Nesterov的单调变异不平等的加速预计梯度方法
A Nesterov's Accelerated Projected Gradient Method for Monotone Variational Inequalities
论文作者
论文摘要
在此技术说明中，我们关注的是解决融合率提高的变异不平等的问题。由Nesterov的加速梯度方法进行凸优化，我们提出了Nesterov的加速投影梯度算法，以解决变异不平等问题。我们证明，在Lipschitz连续性和强烈单调性的共同假设下，所提出的算法至少具有线性速率的收敛性。据我们所知，这是Nesterov加速协议的收敛性首次被证明是针对变异不平等的，除了凸优化或单调包容问题之外。给出了模拟结果，以证明与众所周知的投影梯度方法，反映的投影方法和黄金比率方法相比，所提出的算法的表现要优于表现。结果表明，在我们提出的算法中，达到溶液的所需迭代数量大大减少了。
In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated projected gradient algorithm for variational inequality problems. We prove convergence of the proposed algorithm with at least linear rate under the common assumption of Lipschitz continuity and strongly monotonicity. To the best of our knowledge, this is the first time that convergence of the Nesterov's accelerated protocol is proved for variational inequalities, other than the convex optimization or monotone inclusion problems. Simulation results are given to demonstrate the outperformance of the proposed algorithms over the well-known projected gradient approach, the reflected projected approach, and the golden ratio method. It is shown that the required number of iterations to reach the solution is greatly reduced in our proposed algorithm.
