The focus of this paper is to introduce algorithms with alternated inertial step to solve split feasibility problems. We obtain global convergence of the sequences of iterates generated by the proposed methods under some appropriate conditions. When the split feasibility problem satisfies some bounded linear regularity property, we show that the generated sequences converge linearly. As far as we know, no linear convergence result has been obtained before now for algorithms with inertial steps to solve split feasibility problems in the literature. Our numerical experiments which include a real-world application to jointly constrained Nash equilibrium model show that our methods outperform some inertial methods and other related methods for split feasibility problems in the literature.

本文的重点是介绍具有交替惯性步长的算法来解决分裂可行性问题。我们在某些适当的条件下获得了所提出的方法生成的迭代序列的全局收敛性。当分裂可行性问题满足某些有界线性正则性时，我们证明生成的序列是线性收敛的。据我们所知，到目前为止，对于采用惯性步长的算法来解决分裂可行性问题的文献，还没有获得线性收敛结果。我们的数值实验包括在联合约束的Nash平衡模型中的实际应用，结果表明，我们的方法优于一些惯性方法和其他相关方法，可以解决文献中的分裂可行性问题。