== Problem 1

Results:

#image("prob1.png")

== Problem 2

Original:

$
  frac(1, 2) w^T S w - nu rho + sum_t C^t xi^t
$

Find the Lagrangian first:

$
  frac(1, 2) w^T S w - nu rho + sum_t C^t xi^t
$