A globally convergent trust region multidimensional filter SQP algorithm for nonlinear programming

Abstract

We propose a trust region multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 15 (2005), pp. 17–38] is extended to solve constrained optimization problems. The constraints are partitioned into p parts. The entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but also the individual behaviour of each part of the constraints is considered. The filter's entries and the acceptance criteria are different from other filter-related algorithms in the literature. It should be noted that the undesirable link between the objective function and the constraint violation function in the filter acceptance criteria disappears. Our algorithm is also combined with the non-monotone technique for accepting a trial step, which leads to a more flexible acceptance criteria. Under mild conditions, global convergence is proved. Numerical results show the robustness and efficiency of our algorithm.

Keywords:

• trust region
• multidimensional filter
• SQP
• KKT point
• nonlinear programming

2000 AMS Subject Classifications :

• 90C30
• 90C55
• 90C26
• 65K05
• 49M37

Acknowledgements

This research was supported by the National Science Foundation of China (No. 10771162). We are grateful to the anonymous referees and editor for their useful and detailed comments.