# 推导2

$$
\begin{aligned}
L(a\_1, a\_2) = f(1,1)+2f(1,2)+f(2,2) \\
+2\sum\_{j=3}^Nf(1,j) +2\sum\_{j=3}^Nf(2,j) \\
-a\_1 - a\_2 + \text{常数项}&& {1}
\end{aligned}
$$

其中：

$$
f(i, j) = a\_ia\_jy\_iy\_jK(x\_i,x\_j)
$$

对偶问题中的限制条件也可以分成变量和常量两部分：

$$
\begin{aligned}
\sum\_{i=1}^Na\_iy\_i=a\_1y\_1+a\_2y\_2 + \sum\_{i=3}^Na\_iy\_i = 0 && {2}
\end{aligned}
$$

令常数项为：

$$
\begin{aligned}
\xi = \sum\_{i=3}^Na\_iy\_i && {3}
\end{aligned}
$$

根据公式（3），得到$$a\_1$$和$$a\_2$$的关系为：

$$
a\_1 = \frac {-\xi - a\_2y\_2}{y\_1}
$$


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