Convex Functionals in Open image in new windowp(X)
The importance of geodesically convex functionals in Wasserstein spaces was firstly pointed out by McCann , who introduced the three basic examples we will discuss in detail in 9.3.1, 9.3.4, 9.3.6. His original motivation was to prove the uniqueness of the minimizer of an energy functional which results from the sum of the above three contributions.
KeywordsRelative Entropy Separable Hilbert Space Borel Probability Measure Optimal Transport Lower Semicontinuous Function
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