Duality and column generation

4 important questions on Duality and column generation

What does the primal and the dual generate?

The primal maximization problem generates a LB z and the dual minimization problem generates a UB w;

What is considered weak duality?

W >= Z

What are the consequences of weak duality?

  • When w=z the feasible basic solutions are optimal for the primal and the dual problem;
  • If the primal is unbounded, the dual has no feasible solutions;
  • If the dual is unbounded, the primal has no feasible solution;
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For all slack variables si and dual variables yi what property holds?

Si * yi = 0 for all i

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