Tensor Complementarity Problems—Part II: Solution Methods

2019 ◽  
Vol 183 (2) ◽  
pp. 365-385 ◽  
Author(s):  
Liqun Qi ◽  
Zheng-Hai Huang
Keyword(s):  
Complementarity Problems ◽  
Solution Methods ◽  
Tensor Complementarity ◽  
Tensor Complementarity Problems

Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems

2019 ◽  
Vol 36 (02) ◽  
pp. 1940002 ◽  
Author(s):  
Xue-Li Bai ◽  
Zheng-Hai Huang ◽  
Xia Li
Keyword(s):  
Complementarity Problems ◽  
Stability Of Solutions ◽  
Uniqueness Of Solutions ◽  
Solution Maps ◽  
Upper Semicontinuous ◽  
Tensor Complementarity ◽  
Tensor Complementarity Problems ◽  
The Stability ◽  
The Relationship ◽  
Tensor Variational Inequality

Recently, tensor complementarity problems are becoming more and more popular. There are various literatures considering all kinds of properties of tensor complementarity problems, however, the stability of solutions and the continuity of solution maps are rarely mentioned so far. In the present paper, we study these two properties for tensor complementarity problems. We propose conditions under which the solutions of tensor complementarity problems are stable with the help of the tensor variational inequality or structured tensors. We also show that the solution maps of tensor complementarity problems are upper semicontinuous with the involved tensors being [Formula: see text]-tensors. Meanwhile, we establish the relationship between the uniqueness of solutions and the continuity of solution maps of tensor complementarity problems.

scholarly journals A new smoothing spectral conjugate gradient method for solving tensor complementarity problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
ShiChun Lv ◽  
Shou-Qiang Du
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Complementarity Problem ◽  
Research Work ◽  
Tensor Complementarity Problem ◽  
Solution Methods ◽  
Tensor Complementarity ◽  
Tensor Complementarity Problems ◽  
Spectral Conjugate Gradient

<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>

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