SVMs - Fat (Margin) Boundary: Why is $\max\frac1{||\theta||}=\min \frac{ ||\theta||^2}{2}$?
Minimizing $\|\theta\|$ is equivalent to minimizing $\|\theta\|^2/2$, in the sense that the minimum is achieved for the same value of $\theta$.  Since our goal is primarily to find $\theta$, this substitution is not unreasonable.
Why was the substitution done?  I don't know.  Perhaps because it makes the resulting optimization easier; or just because it seemed simpler.  Note that while $\|\theta\|$ might look &quot;simpler&quot;, in some sense it is an uglier function, as it involves a square root, which can be messy to deal with.  The way to figure out would be to understand the basic derivation using $\|\theta\|^2/2$, and then try replacing with $\|\theta\|$ and see if the same logic goes through or if there is a barrier.