Consider a proof system in which f(x) ≥ v is inferred from the system g(x) ≥ 0 when there is a u ≥ 0 such that ug(x) ≤ f(x)−v −α min{0, ug(x)} for all x ∈ S, where α≥ 0 is fixed. Write the...

Consider a proof system in which f(x) ≥ v is inferred from the system

g(x) ≥ 0 when there is a u ≥ 0 such that ug(x) ≤ f(x)−v −α min{0, ug(x)}

for all x ∈ S, where α≥ 0 is fixed. Write the corresponding inference dual of

(4.16). Show that its solution provides a bound that is no better than that

of the surrogate dual and no worse than that of the Lagrangean dual.