Easy transportation-like problems on K-dimensional arrays
type: Item
instance of: scholarly article
title: Easy transportation-like problems on K-dimensional arrays
zbMATH Open document ID: 0679.90037
DOI: 10.1007/BF00940537
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: The K-dimensional version of two transportation-like problems is posed and efficiently solved. The case \(K=2\) goes as follows: Given an (m,n)- matrix A of reals, a real m-vector u, and a real n-vector v, find a real (m,n) matrix X minimizing \[ either\quad f(X)=\sum^{m}_{i=1}\sum^{n}_{j=1}(X_{ij}-A_{ij})^ 2\quad or\quad g(X)=\max_{ij}\{X_{ij}-A_{ij}\}, \] subject to linear constraints of transportation type, i.e., \[ \sum^{n}_{j=1}X_{ij}=u_ i,\quad i=1,...m,\quad \sum^{m}_{i=1}X_{ij}=v_ j,\quad j=1,...,n. \] In the generalization for any \(K\geq 2\), consideration of the f(X)-type of objective function yields an explicit formula for the optimal solution, whereas for the g(X)-type a one-pass algorithm is proposed.
Mathematics Subject Classification ID: 90C08
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 91B66
Mathematics Subject Classification ID: 90-08
zbMATH DE Number: 4114370
zbMATH Keywords: input-output matrices
zbMATH Keywords: norm minimization
author: David Romero
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00940537
OpenAlex ID: W1988519304
description: scientific article; zbMATH DE number 4114370