Improved smoothing-type methods for the solution of linear programs

Summary.

We consider a smoothing-type method for the solution of linear programs. Its main idea is to reformulate the primal-dual optimality conditions as a nonlinear and nonsmooth system of equations, and to apply a Newton-type method to a smooth approximation of this nonsmooth system. The method presented here is a predictor-corrector method, and is closely related to some methods recently proposed by Burke and Xu on the one hand, and by the authors on the other hand. However, here we state stronger global and/or local convergence properties. Moreover, we present quite promising numerical results for the whole netlib test problem collection.