Mathematics, Optimization, Data Science, Machine Learning, Duality.
is clear that A’ᵀy ≥ 0 also implies Aᵀy ≥ 0 and y ≥ 0. These two conditions, along with the existing condition bᵀy < 0, means that statement 2 of the Farkas variant is false: there does not exist a y such that Aᵀy ≥ 0, y ≥ 0 and bᵀy < 0. Overall proof The combination of the above three steps can