Stochastic-Lazier-Greedy Algorithm for monotone non-submodular maximization

Lu Han, ,Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China, Min Li, Dachuan Xu, Dongmei Zhang, ,School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P.R. China, ,Department of Operations Research and Scientific Computing, Beijing University of Technology, Beijing 100124, P.R. China, ,School of Computer Science and Technology, Shandong Jianzhu University, Jinan 250101, P.R. China
2017 Journal of Industrial and Management Optimization  
The problem of maximizing a given set function with a cardinality constraint has widespread applications. A number of algorithms have been provided to solve the maximization problem when the set function is monotone and submodular. However, reality-based set functions may not be submodular and may involve large-scale and noisy data sets. In this paper, we present the Stochastic-Lazier-Greedy Algorithm (SLG) to solve the corresponding nonsubmodular maximization problem and offer a performance
more » ... er a performance guarantee of the algorithm. The guarantee is related to a submodularity ratio, which characterizes the closeness of to submodularity. Our algorithm also can be viewed as an extension of several previous greedy algorithms. 2010 Mathematics Subject Classification. Primary: 58F15, 58F17; Secondary: 53C35.
doi:10.3934/jimo.2020085 fatcat:i6qg3msghfgcpnhpt3vrvlf2ii