title: A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints.
abstract: Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one generalized gradient projection explicit formula, which is simple and could reduce the computational cost. Under some mild assumptions, the algorithm possesses the global and strong convergence. Finally, the numerical results show that the proposed algorithm is promising.
authors.affiliation: School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, China.
authors.forename: Guodong
authors.initials: G
authors.lastname: Ma
authors.affiliation: College of Mathematics and Information Science, Guangxi University, Nanning, China.
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, China.
authors.forename: Meixing
authors.initials: M
authors.lastname: Liu
keywords: generalized gradient projection method; global and strong convergence; inequality constraints; minimax optimization problems