Decomposition in large system optimization using the method of multipliers
- 113 Downloads
Although the method of multipliers can resolve the dual gaps which will often appear between the true optimum point and the saddle point of the Lagrangian in large system optimization using the Lagrangian approach, it is impossible to decompose the generalized Lagrangian in a straightforward manner because of its quadratic character. A technique using the linear approximation of the perturbed generalized Lagrangian has recently been proposed by Stephanopoulos and Westerberg for the decomposition. In this paper, another attractive decomposition technique which transforms the nonseparable crossproduct terms into the minimum of sum of separable terms is proposed. The computational efforts required for large system optimization can be much reduced by adopting the latter technique in place of the former, as illustrated by application of these two techniques to an optimization problem of a chemical reactor system.
Key WordsDecomposition techniques generalized Lagrangian large system optimization method of multipliers
Unable to display preview. Download preview PDF.
- 1.Lasdon, L. S.,Optimization Theory for Large Systems, The Macmillan Company, New York, New York, 1970.Google Scholar
- 2.Avery, C. J., andFoss, A. S.,A Shortcoming of the Multilevel Optimization Technique, AIChE Journal, Vol. 17, No. 4, 1971.Google Scholar
- 3.Gould, F. J.,Extensions of Lagrange Multipliers in Nonlinear Programming, SIAM Journal on Applied Mathematics, Vol. 17, No. 6, 1969.Google Scholar
- 4.Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, No. 5, 1969.Google Scholar
- 5.Stephanopoulos, G., andWesterberg, A. W.,The Use of Hestenes' Method of Multipliers to Resolve Dual Gaps in Engineering System Optimization, Journal of Optimization Theory and Applications, Vol. 15, No. 3, 1975.Google Scholar
- 6.Miele, A., Moseley, P. E., Levy, A. V., andCoggins, G. M.,On the Method of Multipliers for Mathematical Programming Problems, Journal of Optimization Theory and Applications, Vol. 10, No. 1, 1972.Google Scholar
- 7.Aris, R.,The Optimal Design of Chemical Reactors, Academic Press, New York, New York, 1961.Google Scholar
- 8.Fan, L. T., andWang, C. S.,The Discrete Maximum Principle, John Wiley and Sons, New York, New York, 1964.Google Scholar
- 9.Goldfarb, D.,Extension of Davidon's Variable Metric Method to Maximization under Linear Inequality and Equality Constraints, SIAM Journal on Applied Mathematics, Vol. 17, No. 4, 1969.Google Scholar
- 10.Fletcher, R., andPowell, M. J. D.,A Rapidly Convergent Descent Method for Minimization, Computer Journal, Vol. 6, No. 2, 1963.Google Scholar