Accelerated reflection projection algorithm and its application to the LMI problem
Accelerated reflection projection algorithm and its application to the LMI problem
复制标题
加速反射投影算法及其在LMI问题中的应用
DOI：
10.1080/02331934.2014.959012
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发表时间：
2015
期刊：
影响因子：
2.2
通讯作者：
Li Xu
中科院分区：
文献类型：
--
作者：
Shin-ya Matsushita;Li Xu
讨论了可用于求解线性矩阵不等式(LMI)问题的交替投影法的加速形式。交替投影法是求解凸可行解问题的一种著名算法，具有许多推广和推广。Bauschke和Kruk提出了一种计算钝锥和闭凸集交点的反射投影算法。我们从两个方向进行这方面的研究。首先，我们给出了反射投影算法的一个加速版本，并证明了它在Hilbert空间中的弱收敛；其次，在一定的假设条件下，我们证明了基于该算法的算法的有限终止性，并给出了所需迭代次数的一个显式上界。通过对LMI问题的数值实验，验证了所提算法的有效性和优点。
We discuss accelerated version of the alternating projection method which can be applied to solve the linear matrix inequality (LMI) problem. The alternating projection method is a well-known algorithm for the convex feasibility problem, and has many generalizations and extensions. Bauschke and Kruk proposed a reflection projection algorithm for computing a point in the intersection of an obtuse cone and a closed convex set. We carry on this research in two directions. First, we present an accelerated version of the reflection projection algorithm, and prove its weak convergence in a Hilbert space; second, we prove the finite termination of an algorithm which is based on the proposed algorithm and provide an explicit upper bound for the required number of iterations under certain assumptions. Numerical experiments for the LMI problem are provided to demonstrate the effectiveness and merits of the proposed algorithms.