The linear programming problem discussed in class involved minimizing

a single artificial variable $$ under the constraints $a^t{y}_i+>b_i$ and $0.$ Show that

the resulting weight vector minimizes the criterion function

$J_{}(a)=ma{x}_{a^t{y}_i}{b}_i[b_i-a^t{y}_i]$

Here, $a$ is the weight vector, $y_i$ are the data vectors, and $b_i$ are the scalar constants.