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An accelerating outer space algorithm for globally solving generalized linear multiplicative problems

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Abstract

This paper proposes an accelerating outer space algorithm for globally solving generalized linear multiplicative problems (GLMP). Utilizing the logarithmic and exponential function properties, we begin with transforming the GLMP into an equivalent problem (EP) by introducing some outer space variables. Then, a two-stage outer space relaxation method is developed to convert the EP into a series of relaxed linear problems. Furthermore, to improve the convergence speed of the algorithm, we develop some accelerating techniques to remove the domains that do not contain a global optimal solution. Then, fusing the linear relaxed method and accelerating techniques into the branch-and-bound framework, we provide the accelerating outer space algorithm for solving the EP. Additionally, we analyze the global convergence of the proposed algorithm. Meanwhile, by investigating the algorithmic complexity, we estimate the maximum iterations required by the proposed algorithm in the worst case. Finally, in contrast to other algorithms in the currently known literature, numerical experimental results indicate that the proposed algorithm is feasible with better efficiency and robustness.

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Acknowledgements

We would like to thank the editor and the reviewers for their helpful suggestions and valuable comments.

Funding

This work is supported by the National Natural Science Foundation of China(61877046) and the Key Scientific and Technological Project of Henan Province (202102210385).

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Authors and Affiliations

  1. School of Computer Science and Technology, Xidian University, Xi’an, 710071, China

    Zhisong Hou

  2. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Sanyang Liu

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  1. Zhisong Hou
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  2. Sanyang Liu
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Zhisong Hou wrote the main manuscript text; All authors reviewed the manuscript.

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Correspondence to Zhisong Hou.

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Hou, Z., Liu, S. An accelerating outer space algorithm for globally solving generalized linear multiplicative problems. Numer Algor 94, 877–904 (2023). https://doi.org/10.1007/s11075-023-01523-y

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  • DOI: https://doi.org/10.1007/s11075-023-01523-y

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