Abstract
In this paper, we propose a new filter algorithm for the system of nonlinear equations. In previous work, the feasibility recovery phase is used to make up for the defect of the filter method, which requires a lot of calculation. To avoid it, the new algorithm is equipped with a new filter. At the same time, we discuss the division of the system of nonlinear equations so that the algorithm can achieve the best numerical results. The new algorithm switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. Combining the new filter with both trust region and line search method, the convergence of the algorithm is obtained. The numerical results show the effectiveness of the new algorithm.
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