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Optimization in the Energy Industry pp 79–130Cite as

New Effective Methods of Mathematical Programming and Their Applications to Energy Problems

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Part of the book series: Energy Systems ((ENERGY))

Summary

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.

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Author information

Authors and Affiliations

  1. Melentiev Energy Systems Institute of SB RAS 130, Lermontov Strasse Irkutsk, Irkutsk, 664033, Russia

    Valerian P. Bulatov

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  1. Valerian P. Bulatov
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Editor information

Editors and Affiliations

  1. Am Mahlstein 8, 67273, Weisenheim, Germany

    Josef Kallrath

  2. Department of Industrial & Systems Engineering, University of Florida, 303 Weil Hall, 116595, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos  & Steffen Rebennack  & 

  3. ProCom GmbH, Luisenstraße 41, 52070, Aachen, Germany

    Max Scheidt

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Bulatov, V.P. (2009). New Effective Methods of Mathematical Programming and Their Applications to Energy Problems. In: Kallrath, J., Pardalos, P.M., Rebennack, S., Scheidt, M. (eds) Optimization in the Energy Industry. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88965-6_5

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  • DOI: https://doi.org/10.1007/978-3-540-88965-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88964-9

  • Online ISBN: 978-3-540-88965-6

  • eBook Packages: EngineeringEngineering (R0)

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