Recall that the hinge loss is

Lhinge$($w$,$x$,$ y $)=$ max$\{0,1$ y $$w $$ Aug$($x $)\}$

The Soft$-$SVM problem aims to minimize the regularized empirical risk:

R$($w $)=$ C

n

n$$

i$=1$

Lhinge$($w$,$x $($i$),$ yi$)+\backslash |$w $\backslash |2$

Show that R$($w $)$ is a convex function of $$w $.$

Hint: you will probably not want to use the formal definition of convexity here. Instead, you$$ll want to show

that R is composed of simpler functions which themselves are convex.