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 you are invited by someone to a wedding banquet, do not sit down at the place of honor, in case someone more distinguished than you has been invited by your host...But when you are invited, go and sit down at the lowest place, so that when your host comes, he may say to you, Friend, move up higher’; then you will be honored in the presence of all who sit at the table with you.”
—Bible: New Testament, Luke 14:8,10.