{"id":{"repo_id":"trento","oai_identifier":"oai:iris.unitn.it:11572/350780"},"canonical_url":"https://search.dev.ndltd.org/etd/trento/oai:iris.unitn.it:11572/350780","repository":{"repo_id":"trento","name":"Università degli Studi di Trento","base_url":"https://iris.unitn.it/oai/request"},"display":{"title":"Some optimal visiting problems: from a single player to a mean-field type model","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Marzufero, Luciano"],"institution":"Università degli studi di Trento","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Bagagiolo, Fabio"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-07-19","date_published":"2022-07-19","updated_at":"2026-07-24T05:04:35Z","subjects":["Optimal control","optimal stopping","optimal switching","mean-field game","continuity equation","transport equation","networks","Settore MAT/05 - Analisi Matematica"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Creative commons","license uri:http://creativecommons.org/licenses/by-nd/4.0/"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://dx.doi.org/10.15168/11572_350780","10.15168/11572_350780"],"render_values":[{"text":"http://dx.doi.org/10.15168/11572_350780","href":"http://dx.doi.org/10.15168/11572_350780","code":true},{"text":"10.15168/11572_350780","href":"https://doi.org/10.15168/11572_350780","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/11572/350780","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Marzufero, Luciano","Bagagiolo, Fabio"]},{"key":"dc:creator","label":"Author","values":["Marzufero, Luciano"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-07-19"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Trento","place:TRENTO"]},{"key":"dc:relation","label":"Dc Relation","values":["firstpage:1","lastpage:114","numberofpages:114"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Optimal control","optimal stopping","optimal switching","mean-field game","continuity equation","transport equation","networks","Settore MAT/05 - Analisi Matematica"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Creative commons","license uri:http://creativecommons.org/licenses/by-nd/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/11572/350780","http://dx.doi.org/10.15168/11572_350780","10.15168/11572_350780"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Some optimal visiting problems: from a single player to a mean-field type model"]}]}],"canonical_facts":{"dc:contributor":["Marzufero, Luciano","Bagagiolo, Fabio"],"dc:creator":["Marzufero, Luciano"],"dc:date":["2022-07-19"],"dc:description":["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. 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