## Scenario Analysis Modeling and Decomposition Methods for Optimization Under Uncertainty |

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### Contents

Modeling examples | 17 |

The progressive hedging algorithm | 30 |

Bundle decomposition method | 47 |

4 other sections not shown

### Common terms and phrases

affine hull algorithm for multi-scenario approximate primal solution approximate solution BT code bundle decomposition algorithm bundle decomposition method bundle method bundle trust region Computational results concave function convergence coupling constraints decomposed decreased defined dual objective function dual problem force unit function f g(yk go to STEP goal programming implemented Inner Iteration line search linear programming problems linearization error MINOS modified bundle decomposition multi-scenario linear programming Mulvey and Vladimirou nonanticipativity constraints null step number of coupling number of force number of iterations Number of Objective objective function value optimal solution orthogonal projection parameter value problem LP1 progressive hedging algorithm proper convex function quadratic programming regularized decomposition regularizing function required number Rockafellar and Wets scenario analysis problem scenario i G X scenario problem Schramm and Zowe search direction serious step set yk+i SPECS files stage decision subgradient test problems Theorem trust region method value sec