In this paper we study variational inequalities defined on a class of structured tensors, and provide existence and uniqueness results. An important special case considered is the nonlinear complementarity problem, recently introduced in the tensor-based form. Both the tensor variational inequality problem and the tensor complementarity problem have application in finding the Nash equilibrium point of the n person noncooperative game. Moreover, we introduce the generalized tensor variational inequalities in the tensor Hilbert space endowed with a inner product between two tensors. At last, we apply this new tool to analyze an extension of the oligopolistic market equilibrium problem.

Variational inequalities on a class of structured tensors

BARBAGALLO, Annamaria
;
GUARINO LO BIANCO, Serena
2018

Abstract

In this paper we study variational inequalities defined on a class of structured tensors, and provide existence and uniqueness results. An important special case considered is the nonlinear complementarity problem, recently introduced in the tensor-based form. Both the tensor variational inequality problem and the tensor complementarity problem have application in finding the Nash equilibrium point of the n person noncooperative game. Moreover, we introduce the generalized tensor variational inequalities in the tensor Hilbert space endowed with a inner product between two tensors. At last, we apply this new tool to analyze an extension of the oligopolistic market equilibrium problem.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/727518
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