Optimization ( IF 2.2 ) Pub Date : 2020-08-06 , DOI: 10.1080/02331934.2020.1797026 Habib ur Rehman, Poom Kumam, Qiao-Li Dong, Yu Peng, Wejdan Deebani
In this paper, we proposed two different methods for solving pseudomonotone and strongly pseudomonotone equilibrium problems. We can examine these methods as an extension and improvement of the Popov's extragradient method. We replaced the second minimization problem onto a closed convex set in the Popov's extragradient method, with a half-space minimization problem that is updated on each iteration and also formulates a useful method for determining the appropriate stepsize on each iteration. The weak convergence theorem of the first method and strong convergence theorem for the second method is well-established based on a standard assumption on a cost bifunction. We also consider various numerical examples to support our well-established convergence results, and we can see that the proposed methods depict a significant improvement in terms of the number of iterations and execution time.
中文翻译:
实 Hilbert 空间中两类均衡规划的一种新的波波夫次梯度超梯度方法
在本文中,我们提出了两种不同的方法来解决伪单调和强伪单调平衡问题。我们可以将这些方法视为波波夫超梯度方法的扩展和改进。我们将第二个最小化问题替换为波波夫超梯度方法中的闭凸集,使用在每次迭代时更新的半空间最小化问题,并且还制定了一种有用的方法来确定每次迭代的适当步长。第一种方法的弱收敛定理和第二种方法的强收敛定理是基于成本双函数的标准假设而建立的。我们还考虑了各种数值例子来支持我们完善的收敛结果,