The paper deals with the study of tensor variational inequalities. and some projection methods to solve them. In particular, some properties on the solutions to such an inequality are established and a fixed point theorem is proved. Moreover, some numerical methods are introduced and the convergence analysis of them is investigated. All the theoretical results are applied to analyze a general oligopolistic market equilibrium problem in which each firm produces several commodities and has some production excesses since the equilibrium condition is characterized by means of a tensor variational inequality. A numerical example is also discussed.
Tensor variational inequalities: Theoretical results, numerical methods and applications to an economic equilibrium model / Barbagallo, A.; Guarino Lo Bianco, S.; Toraldo, G.. - In: JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS. - ISSN 2560-6921. - 4:1(2020), pp. 87-105. [10.23952/jnva.4.2020.1.07]