Mass transportation with LQ cost functions

Details Mass transportation with LQ cost functions Mass transportation with LQ cost functions

2011-05-20

arxiv.org/abs/1105.4037v1

Acta Applicandae Mathematicae 113, 2 (2011) 215-229

Mathematics

Optimization and Control

Scientific paper

10.1007/s10440-010-9595-1

We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem proving existence and uniqueness of an optimal transport map. In the controllable case, we show that the optimal transport map has to be the gradient of a convex function up to a linear change of coordinates. We give regularity results and also investigate the non-controllable case.

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