www-ai.cs.tu-dortmund.de/en/LEHRE/VORLESUNGEN/NOPT/SS14/hw/hw-05.pdf
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 − 2)2, subjet to (x− 1)2 = 5y.
(a) Find all the point satisfying the KKT [...] total homeworks points will be 40.
1.[5] Let h : Rn → Rm be a smooth vector-valued function (each component function hi : Rn → R is continuously differentiable for i = 1, 2, . . . ,m.). Consider the (in [...] (in general nonsmooth) unconstrained optimization problems
min x∈Rn
‖h(x)‖∞, and min x∈Rn
max i=1,...,m
hi(x)
Reformulate each of these problems as a smooth constrained optimization problem.
2.[5] Formulate …