ABSTRACT

In this paper, we introduce a new inertial self-adaptive parallel subgradient extragradient method for finding common solution of variational inequality problems with monotone and Lipschitz continuous operators. The stepsize of the algorithm is updated self-adaptively at each iteration and does not involve a line search technique nor a prior estimate of the Lipschitz constants of the cost operators. Also, the algorithm does not required finding the farthest element of the finite sequences from the current iterate which has been used in many previous methods. We prove a strong convergence result and provide some applications of our result to other optimization problems. We also give some numerical experiments to illustrate the performance of the algorithm by comparing with some other related methods in the literature.

摘要

在本文中，我们介绍了一种新的惯性自适应并行子梯度外梯度方法，用于寻找具有单调和 Lipschitz 连续算子的变分不等式问题的公解。该算法的步长在每次迭代时自适应更新，不涉及线搜索技术，也不涉及成本算子的 Lipschitz 常数的先验估计。此外，该算法不需要在许多以前的方法中使用的当前迭代中找到有限序列的最远元素。我们证明了一个强大的收敛结果，并提供了我们的结果在其他优化问题中的一些应用。通过与文献中其他相关方法的比较，我们还给出了一些数值实验来说明算法的性能。