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A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs

Author

Listed:
  • Yuya Yamakawa

    (Kyoto University)

  • Takayuki Okuno

    (Seikei University
    RIKEN)

Abstract

In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic semidefinite programming (QSDP) subproblems, which we derive from the minimax problem associated with the NSDP. Unlike the existing SQSDP methods, the proposed one allows us to solve those QSDP subproblems inexactly, and each QSDP is feasible. One more remarkable point of the proposed method is that constraint qualifications or boundedness of Lagrange multiplier sequences are not required in the global convergence analysis. Specifically, without assuming such conditions, we prove the global convergence to a point satisfying any of the following: the stationary conditions for the feasibility problem, the approximate-Karush–Kuhn–Tucker (AKKT) conditions, and the trace-AKKT conditions. Finally, we conduct some numerical experiments to examine the efficiency of the proposed method.

Suggested Citation

  • Yuya Yamakawa & Takayuki Okuno, 2022. "A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs," Computational Optimization and Applications, Springer, vol. 83(3), pages 1027-1064, December.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:3:d:10.1007_s10589-022-00402-x
    DOI: 10.1007/s10589-022-00402-x
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    References listed on IDEAS

    as
    1. Qi Zhao & Zhongwen Chen, 2020. "A line search exact penalty method for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 75(2), pages 467-491, March.
    2. Huixian Wu & Hezhi Luo & Xiaodong Ding & Guanting Chen, 2013. "Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 56(3), pages 531-558, December.
    3. A. F. Izmailov & E. I. Uskov, 2017. "Subspace-stabilized sequential quadratic programming," Computational Optimization and Applications, Springer, vol. 67(1), pages 129-154, May.
    4. Li Yang & Bo Yu, 2013. "A homotopy method for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 56(1), pages 81-96, September.
    5. A. Izmailov & M. Solodov & E. Uskov, 2015. "Combining stabilized SQP with the augmented Lagrangian algorithm," Computational Optimization and Applications, Springer, vol. 62(2), pages 405-429, November.
    6. Qi Zhao & Zhongwen Chen, 2018. "An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-25, June.
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    Cited by:

    1. Shun Arahata & Takayuki Okuno & Akiko Takeda, 2023. "Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 555-598, November.

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