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Convergence of a stabilized SQP method for equality constrained optimization

  • Songqiang QiuEmail author
Article
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Abstract

We herein present a stabilized sequential programming method for equality constrained programming. The proposed method uses the concepts of proximal point methods and primal-dual regularization. A sequence of regularized problems are approximately solved with the regularization parameter approaching zero. At each iteration, a regularized QP subproblem is solved to obtain a primal-dual search direction. Further, a trust-funnel-like line search scheme is used to globalize the algorithm, and a global convergence under the weak assumption of cone-continuity property is shown. To achieve a fast local convergence, a specially designed second-order correction (SOC) technique is adopted near a solution. Under the second-order sufficient condition and some weak conditions (among which no constraint qualification is involved), the regularized QP subproblem transits to a stabilized QP subproblem in the limit. By possibly combining with the SOC step, the full step will be accepted in the limit and hence the superlinearly local convergence is achieved. Preliminary numerical results are reported, which are encouraging.

Keywords

Equality constrained optimization Stabilized sequential quadratic programming Trust-funnel-like method Global convergence Local convergence 

Mathematics Subject Classification

90C30 90C55 65K05 

Notes

Acknowledgements

The authors would like to thank the two anonymous referees for their useful comments that helped to improve the original version of the manuscript.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsChina University of Mining and TechnologyXuzhouChina

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