Generalized Dual Decomposition replaces linear regularizers with nonlinear ones in dual decomposition to achieve strong duality and global optimality for mixed-integer two-stage stochastic programs while retaining parallelization.
In this case,α ⊤x+β= P i∈I(x) αi +β= 1− P i∈I( ¯x)\I(x) αi ≤1 becauseα i ≥0, i∈I(x) by the group 2 constraints inE ′
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Generalized Dual Decomposition
Generalized Dual Decomposition replaces linear regularizers with nonlinear ones in dual decomposition to achieve strong duality and global optimality for mixed-integer two-stage stochastic programs while retaining parallelization.