In this paper, we introduce a new general alternative regularization algorithm for solving split equilibrium and fixed point problems in real Hilbert spaces. The proposed method does not require a prior estimate of the norm of the bounded linear operator nor a fixed stepsize for its convergence. Instead, we employ a line search technique and prove a strong convergence result for the sequence generated by the algorithm. A numerical experiment is given to show that the proposed method converges faster in terms of number of iteration and CPU time of computation than some existing methods in the literature.

中文翻译：

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线搜索技术的通用替代正则化方法，用于解决希尔伯特空间中的分裂平衡和不动点问题

在本文中，我们介绍了一种新的通用替代正则化算法，用于解决实际希尔伯特空间中的分裂平衡和不动点问题。所提出的方法不需要对有界线性算子的范数进行先验估计，也不需要其收敛的固定步长。取而代之的是，我们采用线搜索技术，并证明了该算法生成的序列的强大收敛性。数值实验表明，所提出的方法在迭代次数和CPU计算时间上比文献中已有的方法收敛更快。