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Optimal transportation and geometric optics.
Our proof employs the optimal transportation techniques.
In Sect. 4 we focus on applications to optimal transportation and near field geometric optics.
This formulation can find the optimal transportation architecture considering its technology trades over time.
Such problems arise in various applications, notably to optimal transportation, geometric optics and conformal geometry and our critical domain and augmenting matrix convexity notions are adapted from those introduced in [31, 40, 45] for regularity in optimal transportation.
Interest in the general case was stimulated in the last decade through its application to regularity in optimal transportation.
We remark also that the case when Y is independent of u is equivalent to the optimal transportation case.
More applications of the Monge-Ampère equation and the optimal transportation can be found in [3, 4].
By optimal transportation theory and stochastic control, there exists a value of the game with such random strategies.
These conditions were originally formulated for optimal transportation problems in the Monge Ampère case, (k = n), in [31, 45].
The ability to make optimal transportation network investments decision is central to the strategic management of transportation systems.
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