# Why is Hard-margin SVM training a minimization problem rather that a maximization problem?

I am looking at the wikipedia article for hard-margin SVMs and it looks like the optimization problem they use is

"minimize ||w|| such that the classes are linearly separable"

However isn't the point of SVMs to find the hyperplane with the largest margin that separates the datapoints? But since it is trying to minimize ||w|| wouldn't this result in the smallest separating hyperplane? So shouldn't this be a maximization problem rather than a minimization problem?

Because a distance from the origin to a plane is inversely proportional to $$\lVert w \rVert$$, where $$w$$ is a vector normal to the plane. For an appropriate parametrisation, the margin to be maximized is $$2/\lVert w \rVert$$.