Positive-Definite Tensors to Nonlinear Complementarity Problems
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The main purpose of this paper was to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as symmetric positive-definite tensors and copositive tensors, we derive the existence theorems on a solution of these kinds of nonlinear complementarity problems. We prove that a unique solution of the NCP exists under the condition of diagonalizable tensors.
KeywordsCopositive tensor Symmetric tensor Positive-definite tensor Diagonalizable tensors Nonlinear complementarity problems
Mathematics Subject Classification15A18 15A69 65F15 65F10
The authors would like to thank the anonymous referees for their valuable suggestions which help us to improve the manuscript. The first and the third authors are supported by the National Natural Science Foundation of China under Grant 11271084, and the second author was supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 502510, 502111, 501212, 501913).
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