Related papers: Optimal Transport with Defective Cost Functions wi…
We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann's Theorem proving existence and…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces…
We study the Lagrangian formulation of a class of the Monge-Kantorovich optimal transportation problem. It can be considered a stochastic optimal transportation problem for absolutely continuous stochastic processes. A cost function and…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
We consider a spectral optimal design problem involving the Neumann traces of the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset $\Omega$ of $\R^n$. The cost functional measures the amount of energy that Dirichlet…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
In this paper we analyze a mass transportation problem in a bounded domain with the possibility to transport mass to/from the boundary, paying the transport cost, that is given by the Euclidean distance plus an extra cost depending on the…
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional $Q$-curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of…
We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization…
We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form $u \circ \ell$, where $u$ is a suitable monotonically increasing and concave function, and $\ell$ is…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in Let $M$ be a complete Riemnnian manifold and…
We investigate the connections between continuous model theory, free probability, and optimal transport/convex analysis in the context of tracial von Neumann algebras. In particular, we give an analog of Monge-Kantorovich duality for…