Solving LP Problems Via Weighted Centers

Abstract

The feasibility problem for a system of linear inequalities can be converted into an unconstrained optimization problem using ideas from the ellipsoid method, which can be viewed as a very simple minimization technique for the resulting nonlinear function. Using more sophisticated algorithms, we develop and investigate more efficient methods, which lead to two kinds of weighted centers for the feasible set. With these centers, we develop new algorithms for solving linear programming problems.