In this paper, we introduce a numerical iterative algorithm with a reflected step to solve the equilibrium problem, which involves non-monotone bifunctions, in real Hilbert spaces. We give weak convergence analysis when the bifunctions are convex and jointly weakly continuous alongside the associated Minty equilibrium problem with a solution. The assumptions in this paper are weaker than the pseudo-monotonicity Lipschitz-type continuity assumptions used recently on equilibrium problems in the literature. Numerical results on Nash-Cournot equilibrium models show that our algorithm is competitive and efficient.

中文翻译：

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应用于纳什-古诺平衡模型的非单调平衡问题的反射迭代法

在本文中，我们介绍了一种具有反射步长的数值迭代算法来解决真实希尔伯特空间中涉及非单调双函数的平衡问题。当双函数是凸的并且与相关的 Minty 平衡问题一起弱连续时，我们给出了弱收敛分析。本文中的假设弱于最近在文献中用于平衡问题的伪单调性 Lipschitz 型连续性假设。Nash-Cournot 均衡模型的数值结果表明我们的算法具有竞争力和效率。