Relaxed distribution models have recently been proposed by several authors. In this note we point out that Bregman's method may be applied directly to these problems, to yield very simple balancing methods. The convergence of these methods follows directly from Bregman's general proof.
Get full access to this article
View all access options for this article.
References
1.
BacharachM, 1970Biproportional Matrices and Input–Output Change (Cambridge University Press, London)
2.
BregmanL, 1967“The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming”USSR Computational Mathematics and Mathematical Physics7200–217
3.
CensorYLentA, 1978“An iterative row-generation method for interval convex programming” technical report MIGP11, Medical Image Processing Group, Department of Computer Science, State University of New York at Buffalo, Amherst, NY
4.
DaceyM PNorcliffeA, 1977“A flexible doubly-constrained trip distribution model”Transportation Research11203–204
5.
ErikssonJ, 1980a“A note on solution of large sparse maximum entropy problems with linear equality constraints”Mathematical Programming18146–154
6.
ErikssonJ, 1980b“On solving linearly constrained maximum entropy problems” technical report LiTH-MAT-R-1980-14, Linköping Institute of Technology, S-581 83 Linköping, Sweden
7.
JeffersonT RScottC H, 1979“The analysis of entropy models with equality and inequality constraints”Transportation Research13B123–132
8.
JörnstenK, 1979“A relaxed distribution model and its combined distribution and assignment counterpart” technical report LiTH-MAT-R-79-38, Linköping, Sweden
9.
LamondBStewartN F, 1981“Bregman's balancing method”Transportation Research (forthcoming)
10.
MurchlandJ D, 1976“Biproportional problem” Lecture Notes in Traffic Studies 1976: 1:8, Transport Studies Group, University College London, London
11.
RockafellarR T, 1970Convex Analysis (Princeton University Press, Princeton, NJ)
12.
StewartN F, 1979“The effect of round-off error on computed solutions of trip distribution problems”Transportation Research13B217–228
