A line search filter-SQP method with Lagrangian function for nonlinear inequality constrained optimization

In this paper, we propose a line search filter technique in association with sequential quadratic programming (SQP) for solving the nonlinear inequality constrained optimization. The Lagrangian function value instead of the objective function value is used in the filter together with an appropriate infeasibility measure. The search direction which is generated by solving the quadratic programming is decomposed into its normal space and tangential space vectors. Under some reasonable conditions, the global convergence is established for every possible choice of the starting point. By using the Lagrangian function value in the filter, it is shown that the algorithm does not suffer from the Maratos effect without a second order correction, so that local superlinear convergence rate is achieved. Numerical results show that the proposed algorithm is efficient.