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The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization. The feasibility restoration phase, which is always used in the traditional filter method, is not needed. Under mild conditions, global convergence and local superlinear convergence rates are obtained. Numerical results demonstrate that the new algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wächter-Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with the non-monotone technique and second order correction step, it is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved. Numerical results show that the new approach is efficient. [ABSTRACT FROM AUTHOR]