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Decomposition Algorithms for Mathematical Programming and Generalization of the Dantzig-Wolfe Method

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Cybernetics Approaches in Intelligent Systems (CoMeSySo 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 661))

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Abstract

The main result of the paper is the applicability of Dantzig-Wolfe method for Large-Scale Nonlinear Programming with composite (block) structure of the function and constraints. Equivalent transformation of this problem is a task decomposition and coordination. This result allows to propose a new class of decomposition methods, which differ in approximating a feasible solution set of the coordination problem.

The authors propose the modification of the Dantzig-Wolfe algorithm for solving mathematical programming problems, where coordinating solutions is a convex set. It was applied as a decomposition algorithm for a quadratic programming problem. The algorithm was implemented in MS Excel environment and its efficiency was studied and tested. The rate of convergence in the number of global iterations was defined in tests, and it is shown that the proposed algorithm is not significantly different from the Dantzig-Wolfe algorithm in linear block programming.

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References

  1. Tsurkov, V.I.: Decomposition in Large-Scale Problems. Monography, Nauka, Moscow (1981)

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Authors and Affiliations

  1. Altai State University, Lenina Prospect 61, 656049, Barnaul, Russia

    Nikolai Oskorbin & Dmitriy Khvalynskiy

Authors
  1. Nikolai Oskorbin
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  2. Dmitriy Khvalynskiy
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Correspondence to Dmitriy Khvalynskiy .

Editor information

Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

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Oskorbin, N., Khvalynskiy, D. (2018). Decomposition Algorithms for Mathematical Programming and Generalization of the Dantzig-Wolfe Method. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Cybernetics Approaches in Intelligent Systems. CoMeSySo 2017. Advances in Intelligent Systems and Computing, vol 661. Springer, Cham. https://doi.org/10.1007/978-3-319-67618-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-67618-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67617-3

  • Online ISBN: 978-3-319-67618-0

  • eBook Packages: EngineeringEngineering (R0)

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