Abstract
Yuan’s lemma is a basic proposition on homogeneous quadratic function systems. In this note, we extend Yuan’s lemma to the fourth-order tensor system. We first give generalized definition of positive semidefinite of fourth-order tensor, and based on it, an extension of Yuan’s lemma is proposed. As an application, we establish the strong duality result of a class of quadratic semidefinite programming problems using the extended Yuan’s lemma.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No. 11671217) and Natural Science Foundation of Xinjiang (Grant No. 2017D01A14)
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Liqun Qi.
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Yang, Q., Zhou, Y. & Yang, Y. An Extension of Yuan’s Lemma to Fourth-Order Tensor System. J Optim Theory Appl 180, 803–810 (2019). https://doi.org/10.1007/s10957-018-1378-2
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DOI: https://doi.org/10.1007/s10957-018-1378-2
Keywords
- Yuan’s lemma
- S-lemma
- Fourth-order tensor
- Symmetry
- Positive semidefinite
- Quadratic semidefinite programming