Duality: conversion summary#

This is a summary of the recommended approach to convert a primal problem into its dual problem.

First, you convert the primal problem to a standard form:

• Minimisation.

• All constraints of the form $ax\le b$.

• All variables with bound $\ge 0$.

Second, you convert the standard-form primal problem into the dual problem, as illustrated in Fig. 1 and written out in the bullet point list below:

• The primal objective function coefficients, $c_n$, are the dual constraint parameters.

• The primal constraint parameters, $b_m$, are the dual objective function coefficients.

• The primal constraints in $\le$ form lead to dual variables $y_m\le 0$.

• The primal constraints in $=$ form lead to dual variables $y_m$ which are unconstrained / free.

• The primal variables $x_n\ge 0$ lead to dual constraints of $\le$ form.

• The constraint coefficient $a_{mn}$ corresponds to the m-th constraint and n-th variable in the primal problem. It corresponds to the n-th constraint and m-th variable in the dual problem.