Quadratically constraint quadratical algorithm model for nonlinear minimax problems

In this paper, a quadratically approximate algorithm framework for solving general constrained minimax problems is presented. The framework contains the idea of the sequential quadratic programming method, the sequential quadratically constrained quadratic programming method, norm-relaxed method and strong sub-feasible method. The global convergence of the algorithm framework is obtained under the Mangasarian-Fromovitz constraint qualification (MFCQ), and the conditions for superlinear convergence of the algorithm framework are presented under the MFCQ, the constant rank constraint qualification (CRCQ) as well as the strong second-order sufficiency conditions (SSOSC). And quadratic convergence rate is obtained under the MFCQ and SSOSC.