# An Iterative Method for Solving Linear Inequalities

 Title An Iterative Method for Solving Linear Inequalities Publication Type Reports Year of Publication 1995 Authors Stewart G.W Date Published 1995/02/06/ Institution Department of Computer Science, University of Maryland, College Park Keywords Technical Report 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. URL http://drum.lib.umd.edu/handle/1903/355