A diagonal quadratic approximation method for large scale linear programs

An augmented Lagrangian method is proposed for handling the common rows in large scale linear programming problems with block-diagonal structure and linking constraints. Using a diagonal quadratic approximation of the augmented Lagrangian one obtains subproblems that can be readily solved in parallel by a nonlinear primal-dual barrier method for convex separable programs. The combined augmented Lagrangian/barrier method applies in a natural way to stochastic programming and multicommodity networks.