Augmented Lagrangian algorithms for linear programming

We introduce new augmented Lagrangian algorithms for linear programming which provide faster global convergence rates than the augmented algorithm of Polyak and Treti'akov. Our algorithm shares the same properties as the Polyak-Treti'akov algorithm in that it terminates in finitely many iterations and obtains both primal and dual optimal solutions. We present an implementable version of the algorithm which requires only approximate minimization at each iteration. We provide a global convergence rate for this version of the algorithm and show that the primal and dual points generated by the algorithm converge to the primal and dual optimal set, respectively.