黎曼流形上的非精确信赖域算法

Inexact trust-region algorithms on Riemannian manifolds

为求解黎曼流形上的大规模可分离问题,Kasai等人在(Advances of the neural information processing systems, 31, 2018)中提出了使用非精确梯度和非精确Hessian的黎曼信赖域算法,并给出了该算法的迭代复杂度(只有证明思路,没有具体证明)。我们指出在该文献的假设条件下,按照其思路不能证明出相应的结果。本文提出了不同的参数假设,并证明了算法具有类似的迭代复杂度。

To solve the large-scale separable problem on Riemannian manifolds,Kasai et al proposed the Riemannian trust-region algorithm with inexact gradients and inexact Hessians in[Advances of the neural information processing systems,31,2018],as well as the estimate of the iteration complexity of this algorithm(only the outline of the proof is given,without providing specific proof).We note that,under the conditions made in the paper,we can not get the desired result.In the present paper,we propose different assumptions on the parameters and establish a similar iteration complexity of the algorithm.