论文标题
惯性的Krasnoselkii-Mann迭代
Inertial Krasnoselskii-Mann Iterations
论文作者
论文摘要
我们确定了惯性的krasnoselskii-mann迭代的弱收敛性，朝着一个准北方运营商家族的一个共同固定点，以及残留物消失的非质子速率的估计。在准缩合设置中获得了强和线性收敛。在这两种情况下，我们都强调了与非惯性案例的关系，并表明从一个政权到另一个制度是关于参数的假设的连续过程。为惯性原始偶对偶的方法和惯性的三操作算法提供了数值插图，其性能优于其非惯性对应物的性能。
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and show that passing from one regime to the other is a continuous process in terms of the hypotheses on the parameters. Numerical illustrations are provided for an inertial primal-dual method and an inertial three-operator splitting algorithm, whose performance is superior to that of their non-inertial counterparts.
