In this paper, we introduce a new algorithm of multi-step inertial form for approximating a common solution of Split Generalized Mixed Equilibrium Problem (SGMEP) and Minimization Problem (MP) in real Hilbert spaces. Motivated by the multi-step inertial technique, we incorporate the multi-step inertial term to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity and lower semicontinuity of the SGMEP associated mappings, we establish the strong convergence of the scheme. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with the non-inertial version.

中文翻译：

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用于逼近分裂广义混合均衡和最小化问题的公共解的多步惯性算法

在本文中，我们介绍了一种多步惯性形式的新算法，用于逼近真实希尔伯特空间中分裂广义混合均衡问题 (SGMEP) 和最小化问题 (MP) 的通用解。受多步惯性技术的启发，我们结合了多步惯性项来加速所提出方法的收敛。在 SGMEP 相关映射的单调性和下半连续性的标准和温和假设下，我们建立了该方案的强收敛性。给出了一些数值例子来说明我们方法的性能，并将其与非惯性版本进行比较。