Consider the inequality constrained convex optimization problem min fo(r) st. f(x) 0,71 [m]. ER and...

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Consider the inequality constrained convex optimization problem min fo(r) st. f(x) ≤0,71 € [m]. ER" and suppose that r R" and AR satisfy the KKT conditions Show that P A>0 Xf(2)=0 Vlo(x)+(r')=0. i-1 Vo(x¹)(x-z*) 20 Vie[m] Vie[m] Vic ml for all feasible r. Hint: Use the fact that f(x) + f(x) (x-r) ≤ f(x) ≤0 for all ie [m] and for all feasible z by the converity of (fi) Then multiply each of these inequalities by A; and sum them over i [m]. Consider the inequality constrained convex optimization problem min fo(r) st. f(x) ≤0,71 € [m]. ER" and suppose that r R" and AR satisfy the KKT conditions Show that P A>0 Xf(2)=0 Vlo(x)+(r')=0. i-1 Vo(x¹)(x-z*) 20 Vie[m] Vie[m] Vic ml for all feasible r. Hint: Use the fact that f(x) + f(x) (x-r) ≤ f(x) ≤0 for all ie [m] and for all feasible z by the converity of (fi) Then multiply each of these inequalities by A; and sum them over i [m].