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Monotone Splitting Sequential Quadratic Optimization Algorithm with Applications in Electric Power Systems

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Abstract

In this paper, we propose a new sequential quadratic optimization algorithm for solving two-block nonconvex optimization with linear equality and generalized box constraints. First, the idea of the splitting algorithm is embedded in the method for solving the quadratic optimization approximation subproblem of the discussed problem, and then, the subproblem is decomposed into two independent low-dimension quadratic optimization subproblems to generate a search direction for the primal variable. Second, a deflection of the steepest descent direction of the augmented Lagrangian function with respect to the dual variable is considered as the search direction of the dual variable. Third, using the augmented Lagrangian function as the merit function, a new primal–dual iterative point is generated by Armijo line search. Under mild conditions, the global convergence of the proposed algorithm is proved. Finally, the proposed algorithm is applied to solve a series of mid-to-large-scale economic dispatch problems for power systems. Comparing the numerical results demonstrates that the proposed algorithm possesses superior numerical effects and good robustness.

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Acknowledgements

The authors wish to thank the Editor-in-Chief and the two anonymous referees for their very professional reviews and quite useful suggestions, which greatly helped us to improve the original version of this paper. This work was supported by the Natural Science Foundation of China, Grants 11771383 and 11601095, and the Natural Science Foundation of Guangxi Province, Grants 2016GXNSFDA380019 and 2016GXNSFBA380185, as well as the Middle-aged and Young Teachers’ Basic Ability Promotion Project of Guangxi Province, Grant 2017KY0537.

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Authors and Affiliations

  1. College of Science, Guangxi University for Nationalities, Nanning, 530006, China

    Jinbao Jian

  2. College of Electrical Engineering, Guangxi University, Nanning, 530004, China

    Chen Zhang & Linfeng Yang

  3. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Jianghua Yin

  4. School of Mathematics and Statistics, Yulin Normal University, Yulin, 537000, China

    Guodong Ma

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  1. Jinbao Jian
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  2. Chen Zhang
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  3. Jianghua Yin
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  4. Linfeng Yang
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  5. Guodong Ma
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Correspondence to Jinbao Jian.

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Communicated by Jyh-Horng Chou.

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Jian, J., Zhang, C., Yin, J. et al. Monotone Splitting Sequential Quadratic Optimization Algorithm with Applications in Electric Power Systems. J Optim Theory Appl 186, 226–247 (2020). https://doi.org/10.1007/s10957-020-01697-8

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  • DOI: https://doi.org/10.1007/s10957-020-01697-8

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