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Published in:
2009 | OriginalPaper | Chapter
New Effective Methods of Mathematical Programming and Their Applications to Energy Problems
Author : Valerian P. Bulatov
Published in: Optimization in the Energy Industry
Publisher: Springer Berlin Heidelberg
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Convex programming algorithms, which have polynomial-time complexity on the class of linear problems are considered. The paper addresses the Chebyshev points of bounded convex sets, algorithms of their search as well as their different applications in convex programming, for elementary approximations of attainability sets, optimal control, global optimization of additive functions on convex polyhedrons and in the integer programming.
New formulations of energy problems made possible by the following methods are discovered: minimal shutdown during power shortages in a power supply system, search for optimal states in thermodynamic systems, optimal allocation of water resources. The applicability of polynomial-time algorithms to such problems is demonstrated. Consideration is given to the problem of search for the Chebyshev points in multi-criteria models of electric power system expansion and operation.