The hinge loss is a convex function, so many of the usual convex optimizers used in machine learning can work with it. It is not differentiable, but has a subgradient with respect to model parameters w of a linear SVM with score function 
that is given by
The hinge loss is a convex function, so many of the usual convex optimizers used in machine learning can work with it. It is not differentiable, but has a subgradient with respect to model parameters w of a linear SVM with score function that is given by
or the quadratically smoothed
suggested by Zhang.[6] The modified Huber loss is a special case of this loss function with 
.[6]
https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Hinge_loss.html
http://www1.inf.tu-dresden.de/~ds24/lehre/ml_ws_2013/ml_11_hinge.pdf
