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Direct method of hierarchical nonlinear optimization - reassessment after 30 years

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EN
Abstrakty
EN
We consider the optimization problems which may be solved by the direct decomposition method. It is possible when the performance index is a monotone function of other performance indices, which depend on two subsets of decision variables: an individual for every inner performance index and a common one for all. Such problems may be treated as a generalization of separable problems with the additive cost and constraints functions. In the paper both the underlying theory and the basic numerical techniques are presented and compared. A special attention is paid to the guarantees of convergence in different classes of problems and to the effectiveness of calculations.
Rocznik
Tom
Strony
3--11
Opis fizyczny
Bibliogr. 17 poz.
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autor
Bibliografia
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  • [10] W. Findeisen, F. N. Bailey , M. Brdyś, K. Malinowski, P. Tatjewski, and A. Woźniak, Control and Coordination in Hierarchical Systems. Chichester: Wiley, 1980.
  • [11] C. A. Floudas, „Generalized Benders decomposition, GBD", in Encyclopedia of Optimization, C. A. Floudas and P. M. Pardalos, Eds. Dordrecht: Kluwer, 2001, vol. 2, pp. 207-218.
  • [12] C. A. Floudas, A. Aggarwal, and A. R. Ciric, „Global optimum search for nonconvex NLP and MINLP problems", Comput. Chem. Eng., vol. 13, no. 10, pp. 1117-1132, 1989.
  • [13] C. A. Floudas and V. Visweswaran, „A primal-relaxed dual global optimization approach", J. Opt. Theory Appl., vol. 78, no. 2, pp. 187-225, 1993.
  • [14] J. E. Kelley, „The cutting-plane method for solving convex programs", J. Soc. Indust. Appl. Math., vol. 8, pp. 703-712, 1960.
  • [15] A. Nemirovski and D. Yudin, Problem Complexity and Method Efficiency in Optimization. Chichester: Wiley, 1983.
  • [16] N. Z. Shor, Minimization Methods for Non-differentiable Functions. Berlin: Springer Verlag, 1985.
  • [17] Optimization Methods for Large-Scale Systems with Applications, D. A. Wismer, Ed. New York: McGraw-Hill, 1971.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT3-0012-0017
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