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Original Articles

A Decomposition Method Based On The Augmented Lagrangian

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Pages 91-113 | Published online: 25 May 2016

References

  • Bertsekas, D. (1975), Combined primal-dual and penalty methods for constrained minimization, SIAM.J. Control, 13, 3, 521–543.
  • Bertsekas, D. (1983), Constrained Optimization and Lagrange Multiplier Method, Academic Press.
  • Cohen, G. (1978), Optimization by decomposition and coordination: A unified approach, IEEE Trans. Auto. Control, AC-23, 2, 222–232.
  • Cohen, G. and D.L. Zhu (1983), Decomposition coordination methods in large scale optimization problems: The nondifferentiable case and the use of augmented Lagrangians, in J.B. Cruz ed.. Advances in Large Scale Systems; Theory and Applications, JAI Press, Greenwich, Connecticut.
  • Florian, M. and S. Nguyen (1976), Equilibrium traffic assignment methods. Transportation Science, 10, 4, 374–390.
  • Florian, M., J. Guelat and Heinz Speiss (1985), An efficient implementation of the "PARTAN" variant of the linear approximation method for the network equilibrium problem. Pub. No. 395, Centre de Recherche sur les Transports, Univ. de Montreal.
  • Frank, M. and P. Wolfe (1956), An algorithm for quadratic programming, Naval Research Logistics Quarterly, 3, 95–110.
  • Guelat, J. (1983), Algorithms pour le probleme d’affectation du traffic d’equilibre avec demandes fixes, Pub. No. 299, Centre de Recherche sur les Transports, Univ. de Montreal.
  • Gunn, E.A. (1975), An application of linear programming to the planning of woodlands operations. Conference paper, Canadian Operational Research Society Conference May 1975, Waterloo, Ontario.
  • Gunn, E.A., (1987) A decomposition approach to a model of long term forest management. In B. Lev, J. Bloom, A. Gleit and C. Shoemaker, Strategic Planning in Energy and Natural Resources, Elsevier Science Publishers, pp. 319–331.
  • Hestenes, M. (1969), Multiplier and gradient methods, J. Optimization Theory Appl, 4, 5, 303–320.
  • Jomsten, K.O. and P. Varbrand (1985), An augmented Lagrangian approach to multicommodity flow problems with conversions, LiTH-MAT-R-85-16, Department of Mathematics, Linkoping Institute of Technology, Linkoping, Sweden.
  • Lasdon, L. (1970), Optimization Theory for Large Systems, MacMillan.
  • LeBlanc, L. and K. Farhangian (1982), Selection of a trip table which reproduces observed link flows. Transportation Research B, 16B, 2, 83–88.
  • Luenberger, D. (1970), Introduction to Linear and Nonlinear Programming, Addison- Wesley.
  • Meyer, G. (1974), Accelerated Frank-Wolfe algorithm, SIAMJ. Control, 12, 4, 655–663.
  • Miele, A., P. Moseley, A. Levey and G. Coggins (1972), On the method of multipliers for mathematical programming problems, J. Optimization Theory Appl., 10, 1, 1–32.
  • Nguyen, S. (1976), A unified approach to equilibrium methods of traffic assignment. In M. Florian (ed.); Traffic Equilibrium Methods, Proceedings 1974, Vol. 118, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, 148–182.
  • Palacios-Gomez, F., L. Lasdon and M. Enquist (1982), Nonlinear optimization by successive linear programming. Management Science, 28, 10, 1106–1120.
  • Powell, M.J.D. (1969), A method for nonlinear constraints in minimization problems. In R Fletcher, Ed., Optimization, Academic Press, 283–298.
  • Rai, A.K., (1984), ^ Decomposition Approach for a Model of Optimal Forest Management, M.A.SC Thesis, (unpublished), Dept. of Industrial Engineering, Technical University of Nova Scotia, Halifax.
  • Rockafellar, R. (1973), A dual approach to solving nonlinear programming problems. Math Programming, 5, 354–373.
  • Rockafellar, R.T. (1976), Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math of O.R. 1, 2, 97–116.
  • Shapiro, J. (1979), Mathematical Programming: Structures and Algorithms, Wiley Interscience.
  • Thorburn, M. (1984), Decomposition of a Linear Programming Model of Eorest Harvesting and Allocation, M.A.Sc. Thesis, (unpublished), Dept. of Industrial Engineering, Technical University of Nova Scotia, Halifax.
  • Weintraub, A., C. Ortiz, J. Gonzalez (1984), Accelerating convergence of the Frank- Wolfe algorithm, to appear. Transportation Research.
  • Zenetos, P.G. (1986), A Decomposition Approach to Optimal Electric Power System Generation, M.A.Sc. Thesis (unpublished), Dept. of Industrial Engineering, Technical University of Nova Scotia, Halifax.

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