论文标题
惯性外算法的强烈收敛，用于解决变化不平等和固定点问题
Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems
论文作者
论文摘要
该论文研究了两种惯性外算法，以寻求一种通用解决方案，以解决涉及单调和Lipschitz连续映射的变异不平等问题，以及在实际希尔伯特空间中取消取消映射的固定点问题。我们的算法只需要在每次迭代中一次计算可行集合的投影。此外，如果没有成本运算符的Lipschitz常数的先前信息，它们可以很好地工作，并且不包含任何线路搜索过程。算法的强收敛是在合适的条件下建立的。提出了一些实验，以说明建议算法的数值效率，并将其与一些现有算法进行比较。
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms only need to calculate the projection on the feasible set once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the cost operator and do not contain any line search process. The strong convergence of the algorithms is established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.
