In this study, a new algorithm
is presented to solve the following nonlinear minimax problem
This algorithm belongs to the sequential quadratic programming (SQP) type
methods. At each iteration, the search direction d is obtained by solving
one quadratic programming according to the K-T condition of the minimax problem.
When d is equal to zero, then the corresponding iteration point x is a K-T
point, otherwise, d is a descent direction. Unlike the SQP type algorithms
for nonlinear programming, the direction d doesn`t induce any Maratos like
effect. A particular linear search with above-mentioned direction assure global
convergence as well as superlinear convergence. Numerical results to date
suggest the resulting algorithm is effective.