Consider the optimization problem
min 2 x1+ x2
x1 + x2 >= 1
x1 - x2 >= 0
x1,x2>=0
where each xj is a real number. Suppose that an inequality can be inferred from a constraint set if and only if it is a sum of one or more constraints in the set.
Solve the inference dual of (3.9) using this family of proofs. Exhibit the proof that solves the dual. What is the duality gap?