Let f: Rn R be a strongly convex differentiable function so that for some constant a...

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Let f: Rn R be a strongly convex differentiable function so that for some constant a > 0, it - - holds that (Vf(x) - Vf(y))>(x y) a(x y) (x y) for all x and y in R". Let X be a closed convex set in R. Use the variational principle of the minimization problem: minf (x)+q^ x XEX to show that its unique optimal solution is a Lipschitz continuous function of q = Rn. Let f: Rn R be a strongly convex differentiable function so that for some constant a > 0, it - - holds that (Vf(x) - Vf(y))>(x y) a(x y) (x y) for all x and y in R". Let X be a closed convex set in R. Use the variational principle of the minimization problem: minf (x)+q^ x XEX to show that its unique optimal solution is a Lipschitz continuous function of q = Rn.