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strong duality

For a feasible, bounded linear program, the primal and dual optimal values are exactly equal, with no gap.

For a feasible, bounded LP, strong duality strengthens weak duality's inequality to an equality at the optimum: p^*=d^*. Combined with complementary slackness, this is what makes a linear program's dual a genuine certificate of optimality rather than only a lower bound (strong-duality-lp).

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