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)
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“True and false are attributes of speech not of things. And where speech is not, there is neither truth nor falsehood. Error there may be, as when we expect that which shall not be; or suspect what has not been: but in neither case can a man be charged with untruth.”
—Thomas Hobbes (1588–1679)