Given the function:
 
𝑓
(
𝑥
)
=
1
2
𝑥
𝑇
𝑄
𝑥
−
1
𝑚
∑
𝑗
=
1
𝑚
log
⁡
(
1
+
exp
⁡
(
𝑏
𝑗
−
𝑎
𝑗
𝑇
𝑥
)
)
Suppose that 
𝑏
∈
𝑅
𝑚
 and 
𝐴
∈
𝑅
𝑚
×
𝑛
 stack 
{
𝑏
𝑗
}
 and 
{
𝑎
𝑗
𝑇
}
, respectively (rows of 
𝐴
 are 
{
𝑎
𝑗
}
). Derive the mathematical expression for the gradient and Hessian and show how it can be calculated using the Python snippets provided.

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