Consider the min {f (x) : g(x) = 0} where f, g are C1. Prove that every minimizer must be a KKT...

Consider the min {f (x) : g(x) ≥ 0}
where f, g are C1. Prove that every minimizer must be a KKT solution if the
constraints satisfy the Slater condition: functions of g are all concave and
there is an x0 such that g(x0) > 0 (hint: Farkas’ lemma). Slater condition
is one kind of constraint qualification to replace the regularity condition.