## A nested decomposition algorithm with surrogate rows for staircase structured linear programs |

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Abrahamson Ajb2 approach augment basic feasible solution basis for RP1 basis inverse clXl collapsed master problem column proposals complementary slackness convex combination Cornell University corresponding ctxt Dantzig Dantzig-Wolfe decomposition algorithm denote dual infeasible extreme points finite number forward to P2 index the elements iteration of P(t+1 iteration of Pt k'+l k'th iteration lemma linearly independent rows look-ahead cuts Loute m'th master problem P2 matrix nested decomposition nonsingular number of iterations Operations Research optimal for GP optimal solution passed back Peter Jackson price cut primal feasible primal solution Proof Let Proof Suppose Proposition 13 restricted subproblem revised Dantzig-Wolfe decomposition revised decomposition algorithm simplex method solution is optimal solution to GP st+l staircase linear program staircase problem starting basis structured linear programs submatrix surrogate columns surrogate rows surrogate variables Susquehanna University unbounded vector x2 _ Yn+1 Z2 Max zero zj+1