Scenario Analysis Modeling and Decomposition Methods for Optimization Under Uncertainty |
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 g(yk go to STEP implemented Inner Iteration jEJK line search linear programming problems linearization error MINOS modified bundle decomposition multi-scenario linear programming multi-scenario network problems Mulvey and Vladimirou node nonanticipativity constraints null step number of coupling number of force number of iterations objective function value optimal solution orthogonal projection parameter value problem 4.8 problem LP1 progressive hedging algorithm proper convex function quadratic problem quadratic programming regularized decomposition regularizing function Rockafellar and Wets scenario analysis problem scenario problem Schramm and Zowe search direction serious step SPECS files stage decision subgradient subproblems test problems Theorem trust region method value sec