Page "Duality (mathematics)" Paragraph 22

A kind of geometric duality also occurs in optimization theory, but not one that reverses dimensions.

A linear program may be specified by a system of real variables ( the coordinates for a point in Euclidean space R < sup > n </ sup >), a system of linear constraints ( specifying that the point lie in a halfspace ; the intersection of these halfspaces is a convex polytope, the feasible region of the program ), and a linear function ( what to optimize ).

Every linear program has a dual problem with the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa.