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On the R0-Tensors and the Solution Map of Tensor Complementarity Problems

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Abstract

Our purpose is to investigate several properties of the solution map of tensor complementarity problems. To do this, we focus on the R0-tensors and show some results on the local boundedness and the upper semicontinuity. Furthermore, by using a technique from semi-algebraic geometry, we obtain results on the finite-valuedness, the lower semicontinuity, and the local upper-Hölder stability of the map.

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Acknowledgements

The author would like to thank Professor Nguyen Dong Yen for encouragement. The author is grateful to the anonymous referees for their careful readings and valuable suggestions.

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Authors and Affiliations

  1. Division of Mathematics, Phuong Dong University, 171 Trung Kinh Street, Cau Giay, Hanoi, Vietnam

    Vu Trung Hieu

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  1. Vu Trung Hieu
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Correspondence to Vu Trung Hieu.

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Communicated by Liqun Qi.

Dedicated to Professor Boris Mordukhovich on the occasion of his 70th birthday.

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Hieu, V.T. On the R0-Tensors and the Solution Map of Tensor Complementarity Problems. J Optim Theory Appl 181, 163–183 (2019). https://doi.org/10.1007/s10957-018-1441-z

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  • DOI: https://doi.org/10.1007/s10957-018-1441-z

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