Consider the optimization problem min 2x1 + x2 x1 + x2 ≥ 1 x1 − x2 ≥ 0 x1, x2 ≥ 0 (4.3) where each xj is a real number. Suppose that an inequality can be inferred from a constraint set if and only if...

Consider the optimization problem

min 2x1 + x2

x1 + x2 ≥ 1

x1 − x2 ≥ 0

x1, x2 ≥ 0

(4.3)

where each xj is a real number. Suppose that an inequality can be inferred

from a constraint set if and only if it a sum of one or more constraints in the

set. Solve the inference dual of (4.3) using this family of proofs. Exhibit two

proofs, either of which solves the dual. What is the duality gap?