machine learning – What algorithm do SVMs use to minimize their objective function?

Support Vector Machines turn machine learning linear classification tasks into a linear optimization problems.

$$text{minimize } J(theta,theta_0) = frac1n sum_1^n text{HingeLoss}(theta,theta_0) + frac{lambda}{2} ||theta||^2$$

My question is, what linear programming runs on the background for the minimization of the objective function $$J$$. Is it Simplex?