I came across a lecture on Support Vector Machines and in the lecture they converted a maximization problem into a minimization problem. I am wondering how it was done... M a x 1 | | x | | is converted into M i n 1 2 x T xHow was this step achieved..? Many thanks in advance !

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I came across a lecture on Support Vector Machines and in the lecture they converted a maximization problem into a minimization problem. I am wondering how it was done...  M  a  x      1                  |                    |            x              |                    |            is converted into  M  i  n      1    2        x    T    xHow was this step achieved..? Many thanks in advance !

a2g1g9x · Accepted Answer

I know nothing about VSM, but probably this was a constrained optimization problem where it is known that the solution is bounded away from 0 (unconstrained it seems to make little sense). Recall that    (      |        |    x      |        |        )    2    =&amp;lt;  x  ,  x  &amp;gt;=      x          T        x.Now, if   x is bounded away from 0, then maximizing       1                  |                    |            x              |                    |             is the same as minimizing       |        |    x      |        |   (subject to the constraint I assume is missing; and maximizing the square root of a value leads to the same solution as maximizing the value). The factor       1    2   is just for convenience to make the derivative prettier. After you calculate a solution with the factor, you back the solution w/o factor out from it.That&#039;s my guess; but as said, I know nothing about this field.

I came across a lecture on Support Vector Machines and in the lecture they converted a maximization

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