对偶问题:
L(W,b,a) = 1/2 * ||W||^2 + Sum{ ai * (1 - yi * (WTXi + b) ) }
有表达式,凸二次存在极值点
极值点处,偏导为0:
D(L) / D(W) = D( 1/2 * ||W||^2 ) / D(W) + D( Sum{ ai * (1 - yi * (WTXi + b) ) } ) / D(W)
D( 1/2 * ||W||^2 ) / D(W) = W //见2范数求导
D( Sum{ ai * (1 - yi * (WTXi + b) ) } ) / D(W)
D( - Sum{aiyiWTXi} ) / D(W)
-1 * Sum{ aiyiXi }
结合两部分:
D(L) / D(W) = W - Sum{ aiyiXi }
当D(L) / D(W) 极值点:
D(L) / D(W) = W - Sum{ aiyiXi } = 0
即:
W = Sum{aiyiXi}
同理:
0 = Sum{ai*yi}