machine learning optimization

Question

I was studying SVM and I am having problems in the conversion of this optimization problem into another :

and gamma_hat is defined by

I had to paste the images because I was having troubles with MathJax ( Sorry for that ) . Can anyone explain me how the two optimization problems are same . Sorry again for the poor framing of question .

Answer 1

In modern sources, $\hat γ=1$. This amounts to just a rescaling, replacing $w,b$ by $w/γ, b/γ$ and observing that maximizing $γ$ in the previous formulation is the same as minimizing the now variable norm $\|w\|$.

Answer 2

Since $\gamma=\hat\gamma/||w||$, think of this as merely a substitution. But now, you'll see that in the "such that" part, you have $2$ equations, one is just that $||w||=1$, you can account for this by setting $||w||=1$ in the other equation.