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· ‖2 to have the same solution. 3.[10] Consider the problem of finding the point (x, y)T ∈ R2 on the parabola y = (x− 1)2/5 that is closest to (1, 2)T , in the Euclidean norm: min (x,y)T∈R2 (x− 1)2 + (y [...] (y − 2)2, subjet to (x− 1)2 = 5y. (a) Find all the point satisfying the KKT conditions. Is the LICQ satisfied? (b) Which of these are solutions? (c) By directly substituting the constraint into the objective [...] vector-valued function (each component function hi : Rn → R is continuously differentiable for i = 1, 2, . . . ,m.). Consider the (in general nonsmooth) unconstrained optimization problems min x∈Rn ‖h(x)‖∞ …

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