This paper proposes two algorithms that are based on a subgradient and an inertial scheme with the explicit iterative method for solving pseudomonotone equilibrium problems. The weak convergence of both algorithms is well-established under standard assumptions on the cost bifunction. The advantage of these algorithms is that they did not require any line search procedure or any knowledge about bifunction Lipschitz-type constants for step-size evaluation. A practical explanation of this is that they use a sequence of step-size that are revised at each iteration based on some previous iteration. For a numerical experiment, we consider a well-known Nash-Cournot equilibrium model of electricity markets and also other test problems to assist the well-established convergence results and be able to see that our proposed algorithms have a competitive advantage over the time of execution and the number of iterations.

本文提出了两种基于子梯度和惯性方案的算法，采用显式迭代方法求解拟单调平衡问题。在关于成本双功能的标准假设下，这两种算法的弱收敛性都是很好的。这些算法的优势在于，它们不需要任何行搜索程序或任何有关双功能Lipschitz型常数的知识即可进行步长评估。对此的实际解释是，它们使用一系列步长序列，这些步长序列会在每次迭代时基于一些先前的迭代进行修改。对于数值实验，