Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary cond...Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints.By means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix.At each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are solved.Under mild conditions,the proposed algorithm is globally convergent.Finally,some preliminary numerical experiments are reported,and these show that the algorithm is promising.展开更多
基金Supported by the National Natural Science Foundation of China(61572011)Hebei Provience Nature Science Foundation of China(A2018201172)the Key Research Foundation of Education Bureau of Hebei Province(ZD2015069)
基金the Natural Science Foundation of Guangxi Province(2018GXNSFAA281099)the National Natural Science Foundation of China(11771383)the Yulin Normal University Research Grant(2019YJKY16).
文摘Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints.By means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix.At each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are solved.Under mild conditions,the proposed algorithm is globally convergent.Finally,some preliminary numerical experiments are reported,and these show that the algorithm is promising.
