The empirical cost of optimal incomplete transportation
نویسندگان
چکیده
منابع مشابه
Uniqueness and Approximate Computation of Optimal Incomplete Transportation Plans∗
For α ∈ (0, 1) an α−trimming, P ∗, of a probability P is a new probability obtained by re-weighting the probability of any Borel set, B, according to a positive weight function, f ≤ 1 1−α , in the way P ∗(B) = R B f(x)P (dx). If P,Q are probability measures on Euclidean space, we consider the problem of obtaining the best L2−Wasserstein approximation between: a) a fixed probability and trimmed ...
متن کاملThe Decomposition of Optimal Transportation Problems with Convex Cost
Given a positive l.s.c. convex function c : Rd → R and an optimal transference plane π for the transportation problem ∫ c(x′ − x)π(dxdx′), we show how the results of [6] on the existence of a Sudakov decomposition for norm cost c = | · | can be extended to this case. More precisely, we prove that there exists a partition of Rd into a family of disjoint sets {Sh a }h,a together with the projecti...
متن کاملDesigning Incomplete Hub Location-routing Network in Urban Transportation Problem
In this paper, a comprehensive model for hub location-routing problem is proposed which no network structure other than connectivity is imposed on backbone (i.e. network between hub nodes) and tributary networks (i.e. networks which connect non-hub nodes to hub nodes). This model is applied in public transportation, telecommunication and banking networks. In this model locating and routing is c...
متن کاملThe geometry of optimal transportation
A classical problem of transporting mass due to Monge and Kantorovich is solved. Given measures μ and ν on Rd, we find the measure-preserving map y(x) between them with minimal cost — where cost is measured against h(x − y) with h strictly convex, or a strictly concave function of |x − y|. This map is unique: it is characterized by the formula y(x) = x − (∇h)−1(∇ψ(x)) and geometrical restrictio...
متن کاملNumerical enclosures of the optimal cost of the Kantorovitch's mass transportation problem
The problem of optimal transportation was formalized by the French mathematician Gaspard Monge in 1781. Since Kantorovitch, this (generalized) problem is formulated with measure theory. Based on Interval Arithmetic, we propose a guaranteed discretization of the Kantorovitch’s mass transportation problem. Our discretization is spatial: supports of the two mass densities are partitioned into fini...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2013
ISSN: 0091-1798
DOI: 10.1214/12-aop812