A nonmonotonic hybrid algorithm for min-max problem

In this paper nonlinear min-max problems are discussed. Instead of the traditional nonmonotone approach presented by Grippo et al., we use the nonmonotonic technique proposed by Zhang and Hager (SIAM J. Optim. 14(4):1043–1056, 2004), to propose a new nonmonotonic algorithm for min-max problem. Moreover, using hybrid technique can make best use of the advantages of both trust region methods and line search methods. In addition, the new approach can reduce the possibility of solving two quadratic subproblems furthest, and circumvent the difficulties of the Maratos effect occurred in the nonsmooth optimization. Under reasonable conditions, the global convergence and the rate of superlinear convergence are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.