tensor complementarity problem
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2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
ShiChun Lv ◽  
Shou-Qiang Du

<p style='text-indent:20px;'>In recent years, the tensor complementarity problem has attracted widespread attention and has been extensively studied. The research work of tensor complementarity problem mainly focused on theory, solution methods and applications. In this paper, we study the solution method of tensor complementarity problem. Based on the equivalence relation of the tensor complementarity problem and unconstrained optimization problem, we propose a new smoothing spectral conjugate gradient method with Armijo line search. Under mild conditions, we establish the global convergence of the proposed method. Finally, some numerical results are given to show the effectiveness of the proposed method and verify our theoretical results.</p>


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qingyu Zeng ◽  
Jun He ◽  
Yanmin Liu

In this paper, some properties of structured rectangular tensors are presented, and the relationship among these structured rectangular tensors is also given. It is shown that all the V-singular values of rectangular P-tensors are positive. Some necessary and/or sufficient conditions for a rectangular tensor to be a rectangular P-tensor are also obtained. A new subclass of rectangular tensors, which is called rectangular S-tensors, is introduced and it is proved that rectangular S-tensors can be defined by the feasible vectors of the corresponding rectangular tensor complementarity problem.


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