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An optimal matching problem

Ivar Ekeland (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Given two measured spaces ( X , μ ) and ( Y , ν ) , and a third space Z , given two functions u ( x , z ) and v ( x , z ) , we study the problem of finding two maps s : X → Z and t : Y → Z such that the images s ( μ ) and t ( ν ) coincide, and the integral ∫ X u ( x , s ( x ) ) d μ - ∫ Y v ( y , t ( y ) ) d ν is maximal. We give condition on u and v for which there is a unique solution.

An optimal matching problem

Ivar Ekeland (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Given two measured spaces ( X , μ ) and ( Y , ν ) , and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps s : X → Z and t : Y → Z such that the images s ( μ ) and t ( ν ) coincide, and the integral ∫ X u ( x , s ( x ) ) d μ - ∫ Y v ( y , t ( y ) ) d ν is maximal. We give condition on u and v for which there is a unique solution.

Currently displaying 281 – 300 of 2013