2026-09-22T11:14:41Zhttps://iris.unitn.it/oai/requestoai:iris.unitn.it:11572/3507802023-12-22T00:06:23Zcom_11572_237821com_11572_101871col_11572_237822ou_ou00004
Some optimal visiting problems: from a single player to a mean-field type model
Marzufero, Luciano
Marzufero, Luciano
Bagagiolo, Fabio
Optimal control
optimal stopping
optimal switching
mean-field game
continuity equation
transport equation
networks
Settore MAT/05 - Analisi Matematica
In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid control-based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. The model is subsequently adapted to a mean-field game framework, that is when a huge population of agents plays the optimal visiting problem with a controlled dynamics and with costs also depending on the distribution of the population. In particular, we investigate a single continuity equation with possible sinks and sources and the field possibly depending on the mass of the agents. The same problem is also studied on a network framework. More precisely, we study a mean-field game model by proving the existence of a suitable definition of an approximated mean-field equilibrium and then we address the passage to the limit.
2022-07-19
info:eu-repo/semantics/doctoralThesis
http://hdl.handle.net/11572/350780
http://dx.doi.org/10.15168/11572_350780
10.15168/11572_350780
eng
firstpage:1
lastpage:114
numberofpages:114
info:eu-repo/semantics/openAccess
Università degli studi di Trento
place:TRENTO
license:Creative commons
license uri:http://creativecommons.org/licenses/by-nd/4.0/