Optimal Paths Related to Discrete Transport Problems

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dc.contributor.authorSultana, Sharmin
dc.contributor.authorUniversity of Lethbridge, Faculty of Arts and Science
dc.contributor.supervisorMomeni, Abbas
dc.date.accessioned2016-02-12T21:51:34Z
dc.date.available2016-02-12T21:51:34Z
dc.date.issued2015
dc.degree.levelMastersen_US
dc.description.abstractThe transport problem proposed by Monge in the 1780's, was to find the best way to move a pile of soil or rubble to an excavation or fill, with the least effort where the cost of a transport map or the transport plan is generally determined by the integral of some powers of the distance, such as $ \vert x-y \vert ^ p $. But in many cases in real applications, the actual cost is not generally determined by a transport path. Sometimes a ``Y-shaped'' path is less expensive compared to a ``V-shaped path'', to transport items from two starting point to one destination point. Here, we will show that one can transport any Radon probability measure to another Radon probability measure through a general optimal transport path, which is given by a vector measure in our setting. Also, we define a new distance function $d_\alpha$ on the space of probability measures which indeed metrizes the weak* topology of measures. This thesis is an exposition of a paper by Qinglan Xia, ``Optimal paths related to transport problems'', World Scientific, $51(2): 252-289, 2002$.en_US
dc.embargoNoen_US
dc.identifier.urihttps://hdl.handle.net/10133/4413
dc.language.isoen_CAen_US
dc.proquest.subject0405en_US
dc.proquest.subject0984en_US
dc.proquest.subject0501en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentMathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectRadon measureen_US
dc.subjectoptimal transport pathen_US
dc.titleOptimal Paths Related to Discrete Transport Problemsen_US
dc.typeThesisen_US
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