Thursday, June 27, 2024 — 11:00 am — aula M2.5, edificio Matematica
Infinite dimensional tensor variational inequalities and applications
Abstract: The aim of the talk is to introduce tensor variational inequalities in Hilbert spaces. Some existence results, a Minty–Browder-type characterization and continuity theorems are obtained (see [2]). The regularity results allow us to introduce a numerical scheme for computing the time-dependent variational solution. Thanks to a discretization of the time interval, we can use the projection method presented in [1] to solve the static tensor variational inequalities. After that we construct the dynamic solution by using a suitable interpolation. In the second part of the talk, the general dynamic oligopolistic market equilibrium model is studied. More precisely, we apply the theoretical results to establish the existence and regularity of a dynamic equilibrium solution. At last, we provide a numerical example.
References
[1] A. Barbagallo, S. Guarino Lo Bianco, G. Toraldo. Tensor variational inequalities: theoretical results, numerical methods and applications to an economic equilibrium model. J. Nonlinear Var. Anal. 4 (2020), pp. 87–105.
[2] A. Barbagallo, S. Guarino Lo Bianco. Infinite dimensional tensor variational inequalities with applications to an economic equilibrium problem. Optim. Methods Softw. 38 (2023), pp. 1058–1080.