@article {17688, title = {An Iterative Method for Solving Linear Inequalities}, volume = {CS-TR-1833}, year = {1995}, month = {1995/02/06/}, institution = {Department of Computer Science, University of Maryland, College Park}, abstract = {This paper describes and analyzes a method for finding nontrivialsolutions of the inequality $Ax \geq 0$, where $A$ is an $m \times n$ matrix of rank $n$. The method is based on the observation that a certain function $f$ has a unique minimum if and only if the inequality {\it fails to have} a nontrivial solution. Moreover, if there is a solution, an attempt to minimize $f$ will produce a sequence that will diverge in a direction that converges to a solution of the inequality. The technique can also be used to solve inhomogeneous inequalities and hence linear programming problems, although no claims are made about competitiveness with existing methods. }, keywords = {Technical Report}, url = {http://drum.lib.umd.edu/handle/1903/355}, author = {Stewart, G.W.} }