A diagonal quadratic approximation method for large scale linear programs

Authors:
John M. Mulvey;Andrzej Ruszczyński
Affiliations:
Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544, USA;Institute of Automatic Control, Warsaw University of Technology, 00665 Warsaw, Poland
Venue:
Operations Research Letters
Year:
1992

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Abstract

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.