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Generalized Benders Decomposition Method to Solve Big Mixed-Integer Nonlinear Optimization Problems with Convex Objective and Constraints Functions

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  • Andrzej Karbowski

    (Research and Academic Computer Network NASK—National Research Institute, ul. Kolska 12, 01-045 Warsaw, Poland)

Abstract

The paper presents the Generalized Benders Decomposition (GBD) method, which is now one of the basic approaches to solve big mixed-integer nonlinear optimization problems. It concentrates on the basic formulation with convex objectives and constraints functions. Apart from the classical projection and representation theorems, a unified formulation of the master problem with nonlinear and linear cuts will be given. For the latter case the most effective and, at the same time, easy to implement computational algorithms will be pointed out.

Suggested Citation

  • Andrzej Karbowski, 2021. "Generalized Benders Decomposition Method to Solve Big Mixed-Integer Nonlinear Optimization Problems with Convex Objective and Constraints Functions," Energies, MDPI, vol. 14(20), pages 1-18, October.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:20:p:6503-:d:653369
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    References listed on IDEAS

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    Cited by:

    1. Ihnat Ruksha & Andrzej Karbowski, 2022. "Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation," Energies, MDPI, vol. 15(20), pages 1-28, October.

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