An Interior Point Method for Linear Programming Using Weighted Analytic Centers

Let R be the convex subset of x ∈ IRn defined by q linear inequalities where x, aj ∈ IRn and bj ∈ IR. Given a strictly positive vector ω; ∈ IRq, the weighted analytic center xac(ω;) is the minimizer of the strictly convex function over the interior of R. We consider the linear programming problem (LP): max{cTx|x ∈ R}. We give an interior point method for solving the LP that uses weighted analytic centers. We test its performance and limitations using a variety of LP problems. We also compare the method with the well-known logarithmic barrier method.