Convergence of the BFGS-SQP Method for Degenerate Problems

Abstract

In this paper, we propose a BFGS (Broyden–Fletcher–Goldfarb–Shanno)-SQP (sequential quadratic programming) method for nonlinear inequality constrained optimization. At each step, the method generates a direction by solving a quadratic programming subproblem. A good feature of this subproblem is that it is always consistent. Moreover, we propose a practical update formula for the quasi-Newton matrix. Under mild conditions, we prove the global and superlinear convergence of the method. We also present some numerical results.

Keywords:

• BFGS-SQP method
• Global convergence
• Inequality constrained optimization
• Sequential quadratic programming

AMS Subject Classification:

• 90C15
• 90C55

ACKNOWLEDGMENTS

The authors would like to thank the referees for their valuable suggestions on the early version of this paper, the State Key Laboratory of Advanced Design and Manufacture for Vehicle Body of Hunan University since the work was done while the authors were working there. This work was supported by the 973 Project of China granted 2004CB719402 and the National Natural Science Foundation of China via grants 10671060 and 10471036.