In this paper, a new extragradient algorithm is presented to solve the pseudomonotone equilibrium problem with a Bregman–Lipschitz-type condition. The superiority of this algorithm is that it can be performed without any precedent information about the Bregman–Lipschitz coefficients. The weak convergence of the algorithm is determinate under mild assumption, and the strong convergence will be established as the bifunction equilibrium is satisfied in different additional assumptions. In conclusion, we can use the algorithm to find a solution of the variational inequality problem. At the end, several numerical examples are exhibited that demonstrate the efficiency of our method compared to the related methods in the studies.

在本文中，提出了一种新的超梯度算法来解决具有 Bregman-Lipschitz 类型条件的伪单调平衡问题。该算法的优势在于它可以在没有任何关于 Bregman-Lipschitz 系数的先例信息的情况下执行。该算法的弱收敛性在温和假设下是确定的，强收敛性将在不同附加假设下满足双函数平衡时建立。总之，我们可以使用该算法找到变分不等式问题的解决方案。最后，展示了几个数值例子，证明了我们的方法与研究中的相关方法相比的效率。