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Auxiliary problem principle and decomposition of optimization problems. (English) Zbl 0417.49046

90C55 Methods of successive quadratic programming type
90C25 Convex programming
93A15 Large-scale systems
65K10 Numerical optimization and variational techniques
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[1] Arrow, K. J., andHurwicz, L.,Decentralization and Computation in Resource Allocation, Essays in Economics and Econometrics, Edited by R. W. Pfouts, University of North Carolina Press, Rayleigh, North Carolina, 1960.
[2] Takahara, Y.,Multilevel Approach to Dynamic Optimization, Systems Research Center, Case Western Reserve University, Report No. SRC-50-C-64-18, 1964.
[3] Lasdon, L. S., andSchoeffler, J. D.,A Multilevel Technique for Optimization, Proceedings of the Joint Automatic Control Conference, Troy, New York, 1965.
[4] Brosilow, C. B., Lasdon, L. S., andPearson, J. D.,Feasible Optimization Methods for Interconnected Systems, Proceedings of the Joint Automatic Control Conference, Troy, New York, 1965.
[5] Mesarovic, M. D., Macko, D., andTakahara, Y.,Theory of Hierarchical Multilevel Systems, Academic Press, New York, New York, 1970. · Zbl 0224.93005
[6] Cohen, G.,Optimization by Decomposition and Coordination: a Unified Approach, IEEE Transactions on Automatic Control, Special Issue on Large-Scale Systems, Vol. AC-23, No. 2, 1978. · Zbl 0391.90074
[7] Ekeland, I., andTemam, R.,Convex Analysis and Variational Problems, North-Holland Publishing Company, Amsterdam, Holland, 1970.
[8] Ortega, J. M., andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970. · Zbl 0241.65046
[9] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[10] Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969. · Zbl 0176.12701
[11] Bertsekas, D. P.,Multiplier Methods: A Survey, Automatica, Vol. 12, pp. 133-146, 1976. · Zbl 0321.49027 · doi:10.1016/0005-1098(76)90077-7
[12] Cohen, G., andJoalland, G.,Coordination Methods by the Prediction Principle in Large Dynamic Constrained Optimization Problems, Proceedings of the IFAC Symposium on Large-Scale Systems, Edited by G. Guardabassi and A. Locatelli, Udine, Italy, 1976.
[13] Sundareshan, M. K.,Generation of Multilevel Control and Estimation Schemes for Large-Scale Systems: A Perturbational Approach, IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-7, No. 3, 1977. · Zbl 0353.93011
[14] Cohen, G.,Coordination of Constrained Optimization Problems by Resource Allocation, Ecole des Mines, Centre d’Automatique-Informatique, Internal Report No. A/49, 1972.
[15] Bernhard, P.,Commande Optimale, Décentralisation, et Jeux Dynamiques, Dunod, Paris, France, 1975.
[16] Geoffrion, A. M.,Primal Resource Directive Approach for Optimizing Nonlinear Decomposable Systems, Operations Research, Vol. 18, No. 3, 1970. · Zbl 0201.22301
[17] Gabay, D., andMercier, B.,A Dual Algorithm for the Solution of a Nonlinear Variational Problem via Finite-Element Approximation, Computers and Mathematics with Applications, Vol. 2, pp. 17-40, 1976. · Zbl 0352.65034 · doi:10.1016/0898-1221(76)90003-1
[18] Joalland, G., andCohen, G.,Optimal Control of a Water Distribution Network by Two Multilevel Methods, Proceedings of the 7th IFAC World Congress, Helsinki, Finland, Edited by A. Niemi, Pergamon Press, London, England, 1978.
[19] Bensoussan, A., Lions, J. L., andTemam, R.,Sur les Méthodes de Décomposition, de Décentralisation, et de Coordination et Applications, Méthodes Numériques d’Analyse de Systèmes, Vol. 2, Cahier IRIA No. 11, 1972.
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