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A Sensitivity Result for Quadratic Second-Order Cone Programming and its Application

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Abstract

In this paper, we present a sensitivity result for quadratic second-order cone programming under the weak form of second-order sufficient condition. Based on this result, we analyze the local convergence of an SQP-type method for nonlinear second-order cone programming. The subproblems of this method at each iteration are quadratic second-order cone programming problems. Compared with the local convergence analysis done before, we do not need the assumption that the Hessian matrix of the Lagrangian function is positive definite. Besides, the iteration sequence which is proved to be superlinearly convergent does not contain the Lagrangian multiplier.

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Acknowledgments

The paper was written when the first author was at the University of Portsmouth as an academic visitor (February 2019–January 2020). The first author wishes to express his sincere thanks to Dr Chee Khian Sim for his advice and help. We would also like to thank the editor and the anonymous referees for their valuable and helpful comments that have improved the quality of this paper greatly.

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Authors and Affiliations

  1. Jiangsu University of Science and Technology, Zhenjiang, 212001, P.R. China

    Qi Zhao

  2. School of Mathematical Sciences, Soochow University, Suzhou, 215006, P.R. China

    Wenhao Fu & Zhongwen Chen

Authors
  1. Qi Zhao
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  2. Wenhao Fu
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  3. Zhongwen Chen
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Corresponding author

Correspondence to Zhongwen Chen.

Additional information

The work was supported by Chinese NSF grant 11871362 and Overseas Study Fund and Start-up Fund for doctoral research by Jiangsu University of Science and Technology.

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Zhao, Q., Fu, W. & Chen, Z. A Sensitivity Result for Quadratic Second-Order Cone Programming and its Application. Appl Math 66, 413–436 (2021). https://doi.org/10.21136/AM.2020.0278-19

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  • DOI: https://doi.org/10.21136/AM.2020.0278-19

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