Hw5 ex1 - norm minimization: Difference between revisions
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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 ?
A The minimization of the square root of the norm is difficult, but it's doable by just taking the derivative of the function; though one will have the same result by minimizing just , where with this notation we mean .
Note that in the literature, is generally already defined as .
--Elisa
