TY - JOUR

T1 - Solution of some transportation problems with relaxed or additional constraints

AU - Rachev, S. T.

AU - Ruschendorf, L.

PY - 1994

Y1 - 1994

N2 - The authors consider some modifications of the usual transportation problem by allowing bound for the admissible supply-respectively, demand--distributions. In particular, the case that the marginal distribution function of the supply is bounded below by a df F1, while the marginal df of the demand is bounded above by a df is considered. For the case that the difference of the marginals is fixed-this is an extension of the well-known Kantorovich--Rubinstein problem--the authors obtain new and general explicit results and bounds, even without the assumption that the cost function is of Monge type. The multivariate case is also treated. In the last section, the authors study Monge-Kantorovich problems with constraints of a local type, that is, on the densities of the marginals. In particular, the classical Dobrushin theorem on optimal couplings is extended with respect to total variation.

AB - The authors consider some modifications of the usual transportation problem by allowing bound for the admissible supply-respectively, demand--distributions. In particular, the case that the marginal distribution function of the supply is bounded below by a df F1, while the marginal df of the demand is bounded above by a df is considered. For the case that the difference of the marginals is fixed-this is an extension of the well-known Kantorovich--Rubinstein problem--the authors obtain new and general explicit results and bounds, even without the assumption that the cost function is of Monge type. The multivariate case is also treated. In the last section, the authors study Monge-Kantorovich problems with constraints of a local type, that is, on the densities of the marginals. In particular, the classical Dobrushin theorem on optimal couplings is extended with respect to total variation.

UR - http://www.scopus.com/inward/record.url?scp=0028427646&partnerID=8YFLogxK

U2 - 10.1137/S0363012991221365

DO - 10.1137/S0363012991221365

M3 - Article

AN - SCOPUS:0028427646

SN - 0363-0129

VL - 32

SP - 673

EP - 689

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 3

ER -