The Linear Case
Linear programming problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is a linear combination of n variables. There are m constraints, each of which places an upper bound on a linear combination of the n variables. The goal is to maximize the value of the objective function subject to the constraints. A solution is a vector (a list) of n values that achieves the maximum value for the objective function.
In the dual problem, the objective function is a linear combination of the m values that are the limits in the m constraints from the primal problem. There are n dual constraints, each of which places a lower bound on a linear combination of m dual variables.
Read more about this topic: Duality (optimization)
Famous quotes containing the word case:
“When trying a case [the famous judge] L. Cassius never failed to inquire “Who gained by it?” Man’s character is such that no one undertakes crimes without hope of gain.”
—Marcus Tullius Cicero (106–43 B.C.)