## Advances in a Nested Decomposition Algorithm for Solving Staircase Linear Programs |

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artificial basic variables basis for period chapter chosen cut chosen point constraints convex combination corresponding cost row ctxt cut is imposed cut on period cut passes Dantzig-Wolfe decomposition determine the chosen dual decomposition dual feasible solution dual ray enhanced algorithm extra column extreme points facet FASTPASS feasibility cut feasible region forward pass full basis full staircase implemented initial main step master master/sub test matrix objective value old cuts optimal basis optimal dual solution optimal primal optimal solution optimality cut passed to period performed period optimizations period t problem period t—1 period t+l perturbed primal and dual primal solution Proof ratio test Resolution Linear Program RHS's SCAGR7 SCB8 shuffle simplex method slack cuts slack variable solution to period Staircase Linear Programs strategy sub-problem surplus columns surplus variables surrogate columns surrogate variables technique test problems Theorem unenhanced variables in period vector violated zero