The Duality Theorem for Rectified Cost Functions
speaker: Aldo Pratelli (Università di Pisa)abstract: The dual problem in mass transportation is very important and well studied, and one says that duality holds if the extremals of the primal and of the dual problem are the same. It is well known that duality holds in a great generality, for instance when the cost function is l.s.c., or bounded. Moreover, simple examples show that duality does not hold in a complete generality. We will introduce a suitable notion of "rectification" of a cost functions, in such a way that duality always holds with the rectified cost. Moreover, the rectification does not change the value of the dual problem, but it only "corrects" the value of the primal one, and optimal transport plans always exist for the rectified cost function. The role of the lower semi-continuity in this operation will be also discussed.
timetable:
Tue 12 Oct, 14:30 - 15:20, Aula Dini
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