论文标题
一类非平滑比总和优化问题的惯性近端块坐标方法
Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems
论文作者
论文摘要
在本文中，我们考虑了一类非平滑比率的分数优化问题，该问题与块结构。该模型类无处不在，并包含文献中几个重要的非平滑优化问题。我们首先提出了一种通过利用基础结构来解决此类问题的惯性近端层坐标方法。在Kurdyka-lojasiewicz（KL）属性和一些温和的假设下，我们的方法的全球融合可以保证。然后，我们确定三个重要的结构化分数优化问题的KL属性的明确指数。特别是，对于基数正则化或稀疏性约束的稀疏广义特征值问题，我们表明KL指数为1/2，因此，所提出的方法表现出线性收敛速率。最后，我们通过分析和模拟的数值示例来说明我们的理论结果。
In this paper, we consider a class of nonsmooth sum-of-ratios fractional optimization problems with block structure. This model class is ubiquitous and encompasses several important nonsmooth optimization problems in the literature. We first propose an inertial proximal block coordinate method for solving this class of problems by exploiting the underlying structure. The global convergence of our method is guaranteed under the Kurdyka--Lojasiewicz (KL) property and some mild assumptions. We then identify the explicit exponents of the KL property for three important structured fractional optimization problems. In particular, for the sparse generalized eigenvalue problem with either cardinality regularization or sparsity constraint, we show that the KL exponents are 1/2, and so, the proposed method exhibits linear convergence rate. Finally, we illustrate our theoretical results with both analytic and simulated numerical examples.
