应用于传感器网络定位的黎曼降维二阶方法

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2024-06-17 DOI:10.1137/23m1567229
Tianyun Tang, Kim-Chuan Toh, Nachuan Xiao, Yinyu Ye
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引用次数: 0

摘要

SIAM 科学计算期刊》,第 46 卷第 3 期,第 A2025-A2046 页,2024 年 6 月。 摘要本文提出了一种立方规则化黎曼优化方法(RDRSOM),该方法部分利用了二阶信息,达到了[math]的迭代复杂度。为了降低每次迭代的计算成本,我们进一步提出了 RDRSOM 的实用版本,它是著名的 Barzilai-Borwein 方法的扩展,可达到 [math] 的最坏情况迭代复杂度。此外,在更严格的条件下,RDRSOM 还能达到 [math] 的迭代复杂度。我们将我们的方法应用于解决无线传感器网络定位问题的一个非线性问题,该问题的可行集是一个黎曼流形,之前的文献从未考虑过这个问题。通过数值实验,我们验证了与最先进的黎曼优化方法和其他非线性求解器相比,我们的算法具有很高的效率。
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A Riemannian Dimension-Reduced Second-Order Method with Application in Sensor Network Localization
SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A2025-A2046, June 2024.
Abstract. In this paper, we propose a cubic-regularized Riemannian optimization method (RDRSOM), which partially exploits the second-order information and achieves the iteration complexity of [math]. In order to reduce the per-iteration computational cost, we further propose a practical version of RDRSOM which is an extension of the well-known Barzilai–Borwein method, which enjoys the worst-case iteration complexity of [math]. Moreover, under more stringent conditions, RDRSOM achieves the iteration complexity of [math]. We apply our method to solve a nonlinear formulation of the wireless sensor network localization problem whose feasible set is a Riemannian manifold that has not been considered in the literature before. Numerical experiments are conducted to verify the high efficiency of our algorithm compared to state-of-the-art Riemannian optimization methods and other nonlinear solvers.
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来源期刊
CiteScore
7.20
自引率
4.30%
发文量
567
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