Difference between revisions of "Hw5 ex1 - norm minimization"
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'''Q''' How do we solve the minimization problem for <math>\sqrt{ || \dot{x} ||}</math>? | '''Q''' How do we solve the minimization problem for <math>\sqrt{ || \dot{x} ||}</math>? | ||
| − | '''A''' The minimization of the square root of the norm is difficult; though one will have the same result by minimizing just <math>|| \dot{x} || </math>, where with this notation we mean <math> \dot{x}^T \dot{x} </math> | + | '''A''' The minimization of the square root of the norm is difficult, but it's doable by just taking the derivative of the <math>\sqrt{\cdot}</math> function; though one will have the same result by minimizing just <math>|| \dot{x} || </math>, where with this notation we mean <math> \dot{x}^T \dot{x} </math>. |
| + | |||
| + | Note that in the literature, <math>|| \dot{x} || </math> is generally already defined as <math>\sqrt{ \dot{x}^T \dot{x} }</math>. | ||
Revision as of 02:34, 12 February 2007
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, \(|| \dot{x} || \) is generally already defined as \(\sqrt{ \dot{x}^T \dot{x} }\).
--Elisa
