Soft margin hyperplanes. The function of the slack variables used inPthe op$-$ timization problem for sofPt margin hyperplanes has the form: $7$ mi$=1$ i$.$ Instead, we could use $7$ mi$=1$ ip$,$ with p $>1.$

$($a$)$ Give the dual formulation of the problem in this general case.

$($b$)$ How does this more general formulation $($p $>1)$ compare to the standard setting $($p $=1)?$ In the case p $=2$ is the optimization still convex?