×

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


MSC:

90C55 Methods of successive quadratic programming type
90C25 Convex programming
93A15 Large-scale systems
65K10 Numerical optimization and variational techniques
PDFBibTeX XMLCite
Full Text: DOI

References:

[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.