# Appendix s1 We introduce a simple optimization procedure for the

```Appendix s1
We introduce a simple optimization procedure for the support vector machine as
described in Equation (5). Recall that objective is
n
1
2
πΊ(π) = min [ ||π|| + πΆ β max(1 β yi π T Xi , 0)]
π 2
i=1
Because it is not strictly monotonic, we can calculate the subgradient directions of
the objective function as follows,
0 βπ¦π π π ππ < β1
ππΊ
π¦π ππ
=π+β
β
π¦π π π ππ = 1
ππ
2
π
{ βπ¦π ππ βπ¦π π π ππ > β1
and iteratively optimize the support vector machine objective.
Algorithm 1: Subgradient descent optimization for SVM
Input: Features πΏ, labels π, parameter πΆ, precision π
Output: Learned weight parameters π
1. Initilaize weight parameters π with random values ranging from 0 to 1.
ππΊ
2. For all elements ππ β πΏ, π¦π β π calculate Ξπ = ππ using the equation
above the algorithm.
3. Update ππ‘+1 = ππ‘ + πΞπ, where π‘ is an index for the iteration and π is a
step size parameter (i.e., a small number like 0.01)
4. If the maximum difference between ππ‘+1 and ππ‘ is smaller than the
precision π, terminate the algorithm and return outputs. Otherwise, iterate
step 2-3 until convergence.
```
Number theory

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