A line search filter SQP method for inequality constrained optimization is presented. This method makes use of a backtracking line search procedure to generate step size and the efficiency of the filter technique to determine step acceptance. At each iteration, the subproblem is always consistent, and it only needs to solve one QP subproblem. Under some mild conditions, the global convergence property can be guaranteed. In the end, numerical experiments show that the method in this paper is effective.
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