Computational Optimization and Applications

, Volume 52, Issue 3, pp 583–607

A nonmonotone filter method for nonlinear optimization


DOI: 10.1007/s10589-011-9430-2

Cite this article as:
Shen, C., Leyffer, S. & Fletcher, R. Comput Optim Appl (2012) 52: 583. doi:10.1007/s10589-011-9430-2


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.


Nonlinear optimizationNonmonotone filterGlobal convergenceLocal convergence

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsShanghai Finance UniversityShanghaiChina
  2. 2.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA
  3. 3.Mathematics DepartmentUniversity of DundeeDundeeUK