The Existence and Uniqueness of Solution for Tensor Complementarity Problem and Related Systems

2021 ◽  
Author(s):  
Lu-Bin Cui ◽  
Yu-Dong Fan ◽  
Yi-Sheng Song ◽  
Shi-Liang Wu
Keyword(s):  
Complementarity Problem ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Tensor Complementarity Problem ◽  
Tensor Complementarity

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>

scholarly journals Solvability of Two Classes of Tensor Complementarity Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Xu ◽  
Weizhe Gu ◽  
He Huang
Keyword(s):  
Complementarity Problem ◽  
Convex Cone ◽  
Complementarity Problems ◽  
Positive Semidefinite ◽  
Closed Convex Cone ◽  
Tensor Complementarity Problem ◽  
Closed Cone ◽  
Strictly Copositive Tensor ◽  
Tensor Complementarity ◽  
Tensor Complementarity Problems

In this paper, we first introduce a class of tensors, called positive semidefinite plus tensors on a closed cone, and discuss its simple properties; and then, we focus on investigating properties of solution sets of two classes of tensor complementarity problems. We study the solvability of a generalized tensor complementarity problem with aD-strictly copositive tensor and a positive semidefinite plus tensor on a closed cone and show that the solution set of such a complementarity problem is bounded. Moreover, we prove that a related conic tensor complementarity problem is solvable if the involved tensor is positive semidefinite on a closed convex cone and is uniquely solvable if the involved tensor is strictly positive semidefinite on a closed convex cone. As an application, we also investigate a static traffic equilibrium problem which is reformulated as a concerned complementarity problem. A specific example is also given.

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