Abstract
In this paper, we propose a feasible-direction method for large-scale nonconvex programs, where the gradient projection on a linear subspace defined by the active constraints of the original problem is determined by dual decomposition. Results are extended for dynamical problems which include distributed delays and constraints both in state and control variables. The approach is compared with other feasible-direction approaches, and the method is applied to a power generation problem. Some computational results are included.
Similar content being viewed by others
References
Lasdon, L. S.,Optimization Theory for Large Systems, The Macmillan Company, London, England, 1970.
Mesarovic, M. D., Macko, D., andTakahara, K.,Theory of Multilevel Hierarchical Systems, Academic Press, New York, New York, 1970.
Wismer, D. A., Editor,Optimization Methods for Large-Scale Systems, with Applications, McGraw-Hill Book Company, New York, New York, 1971.
Tamura, H.,Decentralized Optimization for Distributed-Lag Models of Discrete Systems, Automatica, Vol. 11, pp. 593–602, 1975.
Arrow, K. J., Hurwick, L., andUzawa, H.,Studies in Linear and Nonlinear Programs, Chapter 10, Stanford University Press, Stanford, California, 1958.
Avriel, M.,Nonlinear Programming, Analysis and Methods, Prentice Hall, London, England, 1976.
Rosen, J. B.,The Gradient Projection Method for Nonlinear Programming, Part 1,Linear Constraints, SIAM Journal on Applied Mathematics, Vol. 8, pp. 181–217, 1960.
Zoutendijk, G.,Methods of Feasible Directions, American Elsevier Publishing Company, New York, New York, 1960.
Luenberger, D.,Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973.
Fletcher, R., andReeves, C. M.,Function Minimization by Conjugate Gradients, Computer Journal, Vol. 7, pp. 149–154, 1964.
Tamura, H.,Multistage Linear Programming for Discrete Optimal Control with Distributed Lags, Automatica, Vol. 13, pp. 369–376, 1977.
Lyra, C., Soares, S., andTavares, H.,Controle de Sistemas Hidrotermicos de Geraçao, II Congresso Brasileiro de Automatica, Florianopolis, UFSC, Brasil, 1978.
Turgeon, A.,Optimal Operation of a Hydro-Steam Power System, Cornell University, PhD Thesis, 1975.
Abadie, J.,Application of the GRG Algorithm to Optimal Control Problems, Integer and Nonlinear Programming, Edited by J. Abadie, North Holland Publishing Company, Amsterdam, Holland, 1970.
Mehra, R. K., andDavis, R. E.,A Generalized Gradient Method for Optimal Control Problems with Inequality Constraints and Singular Arcs, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 69–79, 1972.
Author information
Authors and Affiliations
Additional information
Communicated by P. Varaiya
This work was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Brasilia, Brasil, and by the Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo, Brazil.
On leave from UNICAMP, Campinas, Brazil.
Rights and permissions
About this article
Cite this article
Geromel, J.C., Baptistella, L.F.B. Feasible direction method for large-scale nonconvex programs: Decomposition approach. J Optim Theory Appl 35, 231–249 (1981). https://doi.org/10.1007/BF00934578
Issue Date:
DOI: https://doi.org/10.1007/BF00934578