A Primal-Dual Algorithm for MonotropicProgramming and its Application to NetworkOptimization

Authors:
A. Ouorou
Affiliations:
Logilab, HEC Geneva, Section of Management Studies, University of Geneva, 102 Bd Carl-Vogt, CH-1211 Geneva 4, Switzerland. ouorou@hec.unige.ch
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

This paper presents a new primal-dual algorithm forsolving a class of monotropic programming problems. This classinvolves many problems arising in a number of important applicationsin telecommunications networks, transportation and waterdistribution. The proposed algorithm is inspired by Kallio andRuszczyński approach for linear programming [M. Kallio and A.Ruszczyński, WP-94-15, IIASA, 1994]. The problem is replaced bya game using two different augmented Lagrangian functions defined forthe primal and the dual problems. It is then possible to develop ablock-wise Gauss-Seidel method to reach an equilibrium of the gamewith alternating steps made in each component of the primal and dualvariables. Finally, we show how this algorithm may be applied tosome important problems in Network Optimization such as the minimumquadratic cost single flow problems and convex multicommodity flowproblems.