We propose a new nonmonotone filter method to promote global and fast local convergence for sequential quadratic programming algorithms. Our method uses two filters: a standard, global g-filter for global convergence, and a local nonmonotone l-filter that allows us to establish fast local convergence. We show how to switch between the two filters efficiently, and we prove global and superlinear local convergence. A special feature of the proposed method is that it does not require second-order correction steps. We present preliminary numerical results comparing our implementation with a classical filter SQP method.
Shen, C., Leyffer, S., & Fletcher, R. (2012). A nonmonotone filter method for nonlinear optimization. Computational Optimization and Applications, 52(3), 583-607. https://doi.org/10.1007/s10589-011-9430-2