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. - In: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS. - ISSN 1880-5221. - 19:(2018), pp. 711-729.
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.