论文标题
惯性近端方法的弱和强收敛，用于求解二聚体单调平衡问题
Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems
论文作者
论文摘要
在本文中，我们引入了一种惯性近端方法，用于解决涉及希尔伯特空间中两个单调平衡双功能的双重问题。在适当的条件下，没有对轨迹的任何限制性假设，就建立了由迭代方法产生的序列的弱和强收敛。此后，在马鞍点约束下进行了两个特定的案例说明了所提出的方法有关等级最小化问题和平衡问题。此外，给出了一个数值示例来证明我们的算法的可实现性。该算法及其收敛结果改善并发展了现场的先前结果。
In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the iterative method are established. Two particular cases illustrating the proposed method are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under saddle point constraint. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. The algorithm and its convergence results improve and develop previous results in the field.
