Hw5 ex1 - norm minimization

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Q How do we solve the minimization problem for \(\sqrt{ || \dot{x} ||}\)?

A The minimization of the square root of the norm is difficult, but it's doable by just taking the derivative of the \(\sqrt{\cdot}\) function; though one will have the same result by minimizing just \(|| \dot{x} || \), where with this notation we mean \( \dot{x}^T \dot{x} \).

Note that in the literature, \(|| x || \) is generally already defined as \(\sqrt{ x^T x }\).