The nonlinear minimax problems without constraints are discussed. Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. The proposed algorithm does not need any penalty parameters and barrier parameters, and it has small computation cost. In addition, the parameters in the proposed algorithm are few, and the stability of the algorithm is well. Convergence property is described and some numerical results are provided.
Daolan Han. Jinbao Jian. Qinfeng Zhang. "A QP-Free Algorithm for Finite Minimax Problems." Abstr. Appl. Anal. 2014 (SI71) 1 - 9, 2014. https://doi.org/10.1155/2014/436415