Introduction to Tensor Variational Inequalities

2017/01/26 by Yong Wang, Wang, Yong, Zheng‐Hai Huang +3
Engineering · Mathematics · #Advanced Optimization Algorithms Research #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1701.07677

openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a class of variational inequalities, where the involved function is the sum of an arbitrary given vector and a homogeneous polynomial defined by a tensor; and we call it the tensor variational inequality (TVI). The TVI is a natural extension of the affine variational inequality and the tensor complementarity problem. We show that a class of multi-person noncooperative games can be formulated as a TVI. In particular, we investigate the global uniqueness and solvability of the TVI. To this end, we first introduce two classes of structured tensors and discuss some related properties; and then, we show that the TVI has the property of global uniqueness and solvability under some assumptions, which is different from the existed result for the general variational inequality.

Citations

• P-Tensors, P₀-Tensors, and Tensor Complementarity Problem
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• The Sparsest Solutions to Z-Tensor Complementarity Problems

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