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An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming

Author

Listed:
  • Qi Zhao

    (School of Mathematical Science, Soochow University, Suzhou 215006, P. R. China)

  • Zhongwen Chen

    (School of Mathematical Science, Soochow University, Suzhou 215006, P. R. China)

Abstract

A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The l1 exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorithm with the second-order correction step and prove that the fast local superlinear convergence can be obtained under the strict complementarity and the second-order sufficient condition with the sigma term. Finally, some numerical experiments are given to show the effectiveness of the algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:03:n:s0217595918500094
    DOI: 10.1142/S0217595918500094
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    References listed on IDEAS

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    1. Y. Kanno & I. Takewaki, 2006. "Sequential Semidefinite Program for Maximum Robustness Design of Structures under Load Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 265-287, August.
    2. Zhongwen Chen & Shicai Miao, 2015. "A Penalty-Free Method with Trust Region for Nonlinear Semidefinite Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-24.
    3. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
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    Cited by:

    1. 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.

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