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A new projected Barzilai–Borwein method for the symmetric cone complementarity problem

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Abstract

This paper presents a new projected Barzilai–Borwein method for the complementarity problem over symmetric cone by applying the Barzilai–Borwein-like steplengths to the projected method. A new descent direction is employed and a non-monotone line search is used in the method in order to guarantee the global convergence. The projected Barzilai–Borwein method is proved to be globally convergent under some suitable conditions. Some preliminary computational results are also reported which confirm the good theoretical properties of the proposed method.

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Acknowledgements

The funding has been received from National Natural Science Foundation of China with Grant No. 61877046.

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  1. School of mathematics and statistics, Xidian University, Xi’an, 710126, Shaanxi, China

    Xiangjing Liu & Sanyang Liu

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  1. Xiangjing Liu
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  2. Sanyang Liu
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Correspondence to Xiangjing Liu.

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Liu, X., Liu, S. A new projected Barzilai–Borwein method for the symmetric cone complementarity problem. Japan J. Indust. Appl. Math. 37, 867–882 (2020). https://doi.org/10.1007/s13160-020-00424-0

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  • DOI: https://doi.org/10.1007/s13160-020-00424-0

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