半正定Procrustes问题的谱梯度投影法
A Spectral Gradient Projection Method for the Positive Semi-definite Procrustes Problem
摘要：
本文研究半正定procrustes问题（PSDP）。PSDP对应于对称半正定矩阵集上的最小二乘问题。这类问题出现在许多应用中，如结构分析，信号处理等。提出了一种非单调谱投影梯度算法来获得PSDP的数值解。该算法采用Zhang和Hager的非单调技术结合Barzilai和Borwein的步长来加速收敛。给出了一些理论结果。最后通过数值实验验证了所提方法的有效性，并与其他算法进行了比较。
英文摘要：
This paper addresses the positive semi-definite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-definite positive matrices. These kinds of problems appear in many applications such as structure analysis, signal processing, among others. A non-monotone spectral projected gradient algorithm is proposed to obtain a numerical solution for the PSDP. The proposed algorithm employs the Zhang and Hager's non-monotone technique in combination with the Barzilai and Borwein's step size to accelerate convergence. Some theoretical results are presented. Finally, numerical experiments are performed to demonstrate the effectiveness and efficiency of the proposed method, and comparisons are made with other state-of-the-art algorithms.
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