ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Linear inequalities via least squares; pp. 238–248

Full article in PDF format | doi: 10.3176/proc.2013.4.04

Author
Evald Übi

Abstract

The Gaussian elimination method is usually used in solving problems related to systems of linear inequalities. The present review paper describes the application of the least-squares method to studying problems connected with linear inequalities (like redundant inequalities, theorems of alternative, mathematical programming). The minimum norm solution to the system of linear inequalities is found by solving a non-negative least-squares (NNLS) problem. A linear programming (LP) problem is transformed to the system of inequalities in several ways. By solving the corresponding NNLS problem an initial solution to the LP problem is found. The main ideas are explained by simple examples.


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