scholarly journals On the Continuity of the Feasible Set Mapping in Optimal Transport

2020 ◽  
Author(s):  
Mario Ghossoub ◽  
David Saunders
Keyword(s):  
Optimal Transport ◽  
Feasible Set ◽  
Feasible Set Mapping

scholarly journals Lower Semicontinuity of the Feasible Set Mapping of Linear Systems Relative to Their Domains

2012 ◽  
Vol 21 (1) ◽  
pp. 67-92 ◽  
Author(s):  
Aris Daniilidis ◽  
Miguel A. Goberna ◽  
Marco A. López ◽  
Roberto Lucchetti
Keyword(s):  
Linear Systems ◽  
Lower Semicontinuity ◽  
Feasible Set ◽  
Feasible Set Mapping

Calmness of the Feasible Set Mapping for Linear Inequality Systems

2014 ◽  
Vol 22 (2) ◽  
pp. 375-389 ◽  
Author(s):  
M. J. Cánovas ◽  
M. A. López ◽  
J. Parra ◽  
F. J. Toledo
Keyword(s):  
Linear Inequality ◽  
Linear Inequality Systems ◽  
Feasible Set ◽  
Feasible Set Mapping ◽  
Inequality Systems

scholarly journals Stability of the Feasible Set Mapping of Linear Systems with an Exact Constraint Set

2007 ◽  
Vol 16 (5-6) ◽  
pp. 621-635 ◽  
Author(s):  
Jorge Amaya ◽  
Paul Bosch ◽  
Miguel A. Goberna
Keyword(s):  
Linear Systems ◽  
Feasible Set ◽  
Feasible Set Mapping ◽  
Constraint Set ◽  
Exact Constraint

Error bounds for the inverse feasible set mapping in linear semi-infinite optimization via a sensitivity dual approach

Optimization ◽  
2007 ◽  
Vol 56 (5-6) ◽  
pp. 547-563 ◽  
Author(s):  
M. J. Cánovas ◽  
M. A. López ◽  
J. Parra ◽  
F. J. Toledo
Keyword(s):  
Error Bounds ◽  
Dual Approach ◽  
Feasible Set ◽  
Feasible Set Mapping

Characterization of the feasible set mapping in one class of semi-infinite optimization problems

Top ◽  
2004 ◽  
Vol 12 (1) ◽  
pp. 135-147 ◽  
Author(s):  
Estela L. Juárez ◽  
Maxim I. Todorov
Keyword(s):  
Optimization Problems ◽  
Feasible Set ◽  
Feasible Set Mapping

scholarly journals Optimal transport and unitary orbits in C⁎-algebras

2021 ◽  
Vol 281 (5) ◽  
pp. 109068
Author(s):  
Bhishan Jacelon ◽  
Karen R. Strung ◽  
Alessandro Vignati
Keyword(s):  
Optimal Transport ◽  
C Algebras

scholarly journals Modeling Epidemic Spread among a Commuting Population Using Transport Schemes

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1861
Author(s):  
Daniela Calvetti ◽  
Alexander P. Hoover ◽  
Johnie Rose ◽  
Erkki Somersalo
Keyword(s):  
Network Model ◽  
Transport Theory ◽  
Optimal Transport ◽  
State Level ◽  
Compartment Model ◽  
Census Bureau ◽  
Mitigation Strategies ◽  
Mitigation Measures ◽  
Metapopulation Model ◽  
Infection Dynamics

Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.

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