A New Superlinearly Convergent Norm-Relaxed Sqp Method For Constrained Minimax Problems

In this master thesis, the minimax problems with inequality con-straints are discussed, a new fast convergent algorithm for the discussed problems is proposed by means of a new type of line search. The initial point of the proposed method is arbitrary, at each iteration, the main search direction is obtained by solving a quadratic programming (QP) subproblem which always has a solution. Meanwhile, the active set iden-tifying which can reduce the scale and cost of computation is adopted to structure the QP subproblem.In order to avoid the Maratos effect, the high-order correction di-rection is computed by a system of linear equations (SLE). The step size is yielded by a new line search combining the method of strongly sub-feasible direction with penalty method.Without the boundedness assumptions on any of the iterative se-quences, the global convergence can be guaranteed by the new line search and under some mild assumptions. The iteration points can get into the feasible set after a finite number of iterations. Furthermore, the strong and superlinear convergence are obtained under some suitable condi-tions without the strict complementarity. Finally, the proposed method is promising by testing some numerical example.