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Large-Scale Systems and Benders Decomposition
MS&E348Winter 2011/2012
Professor Gerd Infanger
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Block diagonal
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Staircase systems
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Block angular
Primal block angular:connecting constraints +block diagonal D-W decomposition
Dual block angular:connecting variables +block diagonalBenders decomposition
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Benders decomposition (1)
A
B D
The problem
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The subproblem
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Finiteness
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Feasibility
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Feasibility (cont.)
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Outer-linearization
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Full master problem
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Relaxation
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Relaxation (cont.)
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Benders decomposition for linear programs
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Decomposition of the 2-stage stochastic linear program
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L-shaped Method (Van Slyke and Wets, 1969)
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Multi-cut algorithm (Birge and Louveaux, 1985)
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Feasibility
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Benders decomposition (2)
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x
z(x)
The hyper-plane should be support
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Benders decomposition (3)
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