Predictor-Corrector Smoothing Methods for Linear Programs with a More Flexible Update of the Smoothing Parameter

We consider a smoothing-type method for the solution of linear programs. Its main idea is to reformulate the corresponding central path conditions as a nonlinear system of equations, to which a variant of Newton's method is applied. The method is shown to be globally and locally quadratically convergent under suitable assumptions. In contrast to a number of recently proposed smoothing-type methods, the current work allows a more flexible updating of the smoothing parameter. Furthermore, compared with previous smoothing-type methods, the current implementation of the new method gives significantly better numerical results on the netlib test suite.