Abstract

This study examines two different barrier functions and their use in both path-following and potential-reduction interior-point algorithms for solving a linear program of the form: minimize c T x subject to Ax = b and ` x u, where components of ` and u can be nonfinite, so the variables x j can have 0\Gamma; 1\Gamma;or 2-sided bounds, j = 1; :::; n: The barrier functions that we study include an extension of the standard logarithmic barrier function and an extension of a barrier function introduced by Nesterov. In the case when both ` and u have all of their components finite, these barrier functions are \Psi(x) = X j f\Gamma ln(u j \Gamma x j ) \Gamma ln(x j \Gamma ` j )g and \Psi(x) = X j f\Gamma ln(minfu j \Gamma x j ; x j \Gamma ` j g) + minfu j \Gamma x j ; x j \Gamma ` j g=((u j \Gamma ` j )=2)g: Each of these barrier functions gives rise to suitable primal and dual metrics that are used to develop both path-following and potential-reduction interior-point algorithms ...

Citations