Abstract
In this paper, we introduce a cautious BFGS (CBFGS) update criterion in the reduced Hessian sequential quadratic programming (SQP) method. An attractive property of this update criterion is that the generated iterative matrices are always positive definite. Under mild conditions, we get the global convergence of the reduced Hessian SQP method. In particular, the second order sufficient condition is not necessary for the global convergence of the method. Furthermore, we show that if the second order sufficient condition holds at an accumulation point, then the reduced Hessian SQP method with CBFGS update reduces to the reduced Hessian SQP method with ordinary BFGS update. Consequently, the local behavior of the proposed method is the same as the reduced Hessian SQP method with BFGS update. The presented preliminary numerical experiments show the good performance of the method.
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This work was supported by the National Natural Science Foundation of China via grant 10671060 and 10471060.
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Liu, TW., Li, DH. A cautious BFGS update for reduced Hessian SQP. Numer Algor 44, 11–28 (2007). https://doi.org/10.1007/s11075-007-9075-5
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DOI: https://doi.org/10.1007/s11075-007-9075-5