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Globally solving extended trust region subproblems with two intersecting cuts

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Abstract

In this paper, we propose an algorithm to globally solve the extended trust-region subproblem with two linear intersecting cuts. Based on the tightness of the linear cuts at optimal solution, we can resolve the original problem by solving either a traditional trust-region subproblem over a sphere or a semidefinite programming relaxation with second-order cone constraints. Two examples from literature and numerical experiment on randomly generated instances are used to demonstrate how the proposed algorithm works.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their value comments that help improve the quality of this work. Deng’s research has been supported by National Natural Science Foundation of China Grant #11501533 and University of Chinese Academy of Sciences Grant #Y95402MXX2. Lu’s research has been supported by National Natural Science Foundation of China Grants #11701177 and #11771243. Tian’s research has been supported by National Natural Science Foundation of China Grant #71331004 and Fundamental Research Funds for the Central Universities #JBK1805005. Jian’s research has been supported by National Natural Science Foundation of China Grants #71701035 and #71831003.

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Authors and Affiliations

  1. School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China

    Zhibin Deng

  2. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, 100190, China

    Zhibin Deng

  3. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Cheng Lu

  4. School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Ye Tian

  5. School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian, 116025, China

    Jian Luo

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  1. Zhibin Deng
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  2. Cheng Lu
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  3. Ye Tian
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  4. Jian Luo
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Correspondence to Jian Luo.

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Deng, Z., Lu, C., Tian, Y. et al. Globally solving extended trust region subproblems with two intersecting cuts. Optim Lett 14, 1855–1867 (2020). https://doi.org/10.1007/s11590-019-01484-z

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