Decomposition and column generation in integer programming
by JÃ¸rgen Tind
Abstract: The idea of decomposition is a fundamental discipline in mathematical programming with important contributions in theory and
applications. The classical Dantzig-Wolfe and Benders decomposition
procedures based on linear programming duality have had a great impact on research in mathematics, engineering and economics.
The classical ideas can be extended to more general optimization problems by using an appropriate duality theory.
The purpose of this talk is to present a decomposition and column generation procedure in integer programming using integer programming duality. Application of the classical decomposition and column generation
procedure based on linear programming solves the linear programming relaxation of the actual integer programming problem. We shall here demonstrate a procedure leading to an optimal integer solution.
Applications in multicriteria optimization shall be pointed out.
(The presentation is based on joint work with Matthias Ehrgott, The University of Auckland).
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