I don't have a strong math background but I think during the optimisation process of finding the hyperplane, the solver (algorithm that attempts to find best separating hyperplane) uses soft margin to allow mis-classified instances. Its tolerance is controlled by a hyper-parameter so it will comprise to find the best fit within the set parameter. So it is a 'best solution' with a condition. However there are many variations of implementations from different solvers to handle it.

Example:https://towardsdatascience.com/support-vector-machine-simply...