Computational Optimization and Applications

, Volume 52, Issue 3, pp 583-607

First online:

A nonmonotone filter method for nonlinear optimization

  • Chungen ShenAffiliated withDepartment of Applied Mathematics, Shanghai Finance University
  • , Sven LeyfferAffiliated withMathematics and Computer Science Division, Argonne National Laboratory Email author 
  • , Roger FletcherAffiliated withMathematics Department, University of Dundee

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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 optimization Nonmonotone filter Global convergence Local convergence