A J-symmetric quasi-newton method for minimax problems

Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which call J-symmetric method. The is obtained by exploiting structure of second-order derivative objective function in problem. We show that Hessian estimation (as well as its inverse) can be updated rank-2 operation, it turns out update rule natural generalization classic Powell symmetric Broyden from minimization to problems. theory, our proposed algorithm enjoys local Q-superlinear convergence desirable solution under standard regularity conditions. Furthermore, trust-region variant global R-superlinear convergence. Finally, present numerical experiments verify theory effectiveness algorithms compared Broyden’s extragradient on three classes