This paper develops a first-order optimization method for coupled structured matrix factorization (CoSMF) problems that arise in the context of hyperspectral super-resolution (HSR) in remote sensing. To best leverage the problem structures for computational efficiency, we introduce a hybrid inexact block coordinate descent (HiBCD) scheme wherein one coordinate is updated via the fast proximal gradient (FPG) method, while another via the Frank-Wolfe (FW) method. The FPG-type methods are known to take less number of iterations to converge, by numerical experience, while the FW-type methods can offer lower per-iteration complexity in certain cases; and we wish to take the best of both. We show that the limit points of this HiBCD scheme are stationary. Our proof treats HiBCD as an optimization framework for a class of multi-block structured optimization problems, and our stationarity claim is applicable not only to CoSMF but also to many other problems. Previous optimization research showed the same stationarity result for inexact block coordinate descent with either FPG or FW updates only. Numerical results indicate that the proposed HiBCD scheme is computationally much more efficient than the state-of-the-art CoSMF schemes in HSR.

中文翻译：

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用于高光谱超分辨率中耦合结构矩阵分解的混合不精确 BCD

本文开发了一种用于在遥感高光谱超分辨率 (HSR) 背景下出现的耦合结构矩阵分解 (CoSMF) 问题的一阶优化方法。为了最好地利用问题结构来提高计算效率，我们引入了一种混合不精确块坐标下降 (HiBCD) 方案，其中一个坐标通过快速近端梯度 (FPG) 方法更新，另一个坐标通过 Frank-Wolfe (FW) 方法更新。根据数值经验，已知 FPG 类型的方法需要较少的迭代次数来收敛，而 FW 类型的方法在某些情况下可以提供较低的每次迭代复杂度；我们希望充分利用两者。我们表明此 HiBCD 方案的极限点是平稳的。我们的证明将 HiBCD 视为一类多块结构优化问题的优化框架，我们的平稳性主张不仅适用于 CoSMF，还适用于许多其他问题。先前的优化研究表明，仅使用 FPG 或 FW 更新的不精确块坐标下降具有相同的平稳性结果。数值结果表明，所提出的 HiBCD 方案在计算上比 HSR 中最先进的 CoSMF 方案高效得多。