Duality Theory

Duality Theory is an upper bound to the optimal value of the primal problem in every linear programming problem.

P




D





P and D come as a pair implying that the dual to D should be P. x∈Rn is feasible for P, and y∈Rm is feasible for D. You see the direction x→ and y←.

∴

This is Weak Duality Theorem.

Moreover, when the finiteness of the optimal value implies the existence of a solution, this is called The Strong Duality Theorem.



The alphabetical order don't mean anything. It is the direction, min ←.





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