A New Method for Solving Linear Inequalities.
MARYLAND UNIV COLLEGE PARK DEPT OF COMPUTER SCIENCE
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This paper describes a new method for finding nontrivial solutions of the inequality Ax or 0, where A is an mxn 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 fails to have a nontrivial solution. Moreover, if there is a solution, the direction of divergence of an attempt to minimize f will converge to a solution. 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.
- Theoretical Mathematics