Optimal and better transport plans II

  • Date: 06/26/2008
Lecturer(s):

Professor Walter Schachermayer (Vienna University of Technology)

Location: 

University of British Columbia

Topic: 

We consider the Monge-Kantorovick transport problem in a
purely measure theoretic setting, i.e. without imposing continuity
assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and possibly attain infinity. We show that this is true in a more general
setting, in particular for merely Borel measurable cost functions which
are finite almost everywhere on an open set. In a previous paper
Schachermayer and Teichmann considered strongly c-monotone transport plans and proved that every strongly c-monotone transport plan is optimal. We establish necessary and sufficient conditions on c-monotone transport plans to be strongly c-monotone.

Abstracts / Downloads / Reports: 
optimal_and_better_transport_plans.pdf
Other Information: 

Location: WMAX 110

 

PIMS Distinguished Lecturer

 

Note: The paper is on line at http://arxiv.org/abs/0802.0646.

Sponsor: 

pims