Let $(x_1,y_1),(x_2,y_2),$dots$(x_N,y_N)$ be $N$ points on which we find a SVM classifier using the dual SVM formulation which is given below:

Maximize

${\displaystyle \underset{i=1}{\overset{N}{}}}{}_i-{\displaystyle \underset{i=1}{\overset{N}{}}}{\displaystyle \underset{j=1}{\overset{N}{}}}{}_i{}_j{y}_i{y}_j{x}_i{x}_j$

Subject to

${\displaystyle \underset{i=1}{\overset{N}{}}}{}_i{y}_i=0,$ and $,{}_{i}0,$AAi

Let $O_A$ be the value of the objective function at the optimal solution returned by the dual SVM formulation for this problem. Now we add a new point $(x_{N+1},y_{N+1})$ and find a SVM classifier by solving the dual formulation again. Let $O_B$ be the value of the objective function at the optimal solution for this problem. Considering the following three relationships

$(a)O_A>O_R$