Dual Problem - Support Vector Machine - Solution by hand

Question

I am trying to find the solution to the Dual Problem. My data are

]1

with

I solved it using another method and found

But I couldn't solve the Dual Problem. Please tell me what I am doing wrong:

Method 2: Dual Problem

So I got that

Simplifying

Calculating the partials derivatives:

So I ended up with this system

But the solution is a null vector.

Answer 1

Forming the lagrangian

$$ J(\alpha,\lambda) = \sum_k \alpha_k - \frac 12\sum_i\sum_j \alpha_i\alpha_j y_iy_j s_i\cdot s_j+\lambda(\alpha_1+\alpha_2-\alpha_3) $$

the stationary conditions are

$$ \nabla J = 0 = \left\{ \begin{array}{l} -10 \alpha_1-9 \alpha_2+2 \alpha_3+\lambda +1 \\ -9 \alpha_1-25 \alpha_2+7 \alpha_3+\lambda +1 \\ 2 \alpha_1+7 \alpha_2-2 \alpha_3-\lambda +1 \\ \alpha_1+\alpha_2-\alpha_3 \\ \end{array} \right. $$

with solution

$$ \alpha_1 = \frac{11}{50},\ \alpha_2 = \frac{3}{25}, \ \alpha_3 = \frac{17}{50}, \ \lambda = \frac 85 $$