Duality Theory for Multistochastic Monge-Kantorovich Problem

Student: Zimin Aleksandr

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2019

The multistochastic Monge–Kantorovich problem on a product space $X = \prod_{i=1}^n X_i$ is an extension of the classical Monge–Kantorovich problem considered on the space of measures with fixed projections on $X_{i_1} \times \dots \times X_{i_k}$ for all $k$-tuples $\{i_1, \dots, i_k\} \subset \{1, \dots, n\}$, $1 \le k \le n$. In this work we consider well-posedness of the problem, i.e. an existence of a measure on $X$ with given projections. Later we give conditions for existence of a dual solution. Also we give an example without dual solution.

Full text (added May 31, 2019)

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