A survey on theory and algorithms for continuous DR-submodular maximization

The diminishing returns property defines an optimization challenge known as the DR-submodular maximization problem. In the continuous domain, the DR-submodular function holds significant theoretical research value and demonstrates extensive practical relevance across various applications. This type of problem is commonly abstracted from practical scenarios including resource allocation, advertising budget optimization, sensor network, and energy management. In this paper, we discuss classic algorithms for continuous DR-submodular maximization and their variants, covering Frank-Wolfe algorithms, double greedy algorithms, stochastic algorithms, and online algorithms. We also review recent research progress on continuous DR-submodular maximization, providing useful references for further exploration of frontier issues in this field.