结构稀疏优化模型的理论与算法综述
摘要
Structured sparse optimization is one of the most popular research topics in optimization, which has been widely used in a wide range of fields, such as compressed sensing, signal and image processing, machine learning, and biological sciences. In this paper, we first introduce the development of sparse optimization, group sparse optimization, mixed sparse optimization, and joint sparse optimization in recent years. We summarize the theoretical studies and optimization algorithms for structured sparse optimization, including the consistency theory and convergence theory. Finally, we also propose some interesting and important problems in structured sparse optimization that are worthy of further investigation. Generally speaking, a great deal of effort has been achieved in the development of structured sparse optimization; however, there are still several important problems to be resolved.