In this paper, we introduce a new algorithm by incorporating an inertial term with a subgradient extragradient algorithm to solve the equilibrium problems involving a pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert spaces. A weak convergence theorem is well established under certain mild conditions for the bifunction and the control parameters involved. Some of the applications to solve variational inequalities and fixed point problems are considered. Finally, several numerical experiments are performed to demonstrate the numerical efficacy and superiority of the proposed algorithm over other well-known existing algorithms.

中文翻译：

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求解拟单调平衡问题的一般惯性投影型方法的收敛性分析及应用

在本文中，我们引入了一种新的算法，将惯性项与次梯度超梯度算法相结合，以解决实际希尔伯特空间中涉及伪单调和Lipschitz型连续双函数的平衡问题。在某些温和条件下，对于双功能和所涉及的控制参数，已经很好地建立了弱收敛定理。考虑了一些解决变分不等式和定点问题的应用。最后，进行了几个数值实验，以证明该算法在数值上的有效性和优越性。