http://en.wikipedia.org/wiki/Subgradient_method
Classical subgradient rules

Let  be a convex function with domain . A classical subgradient method iterates

where  denotes a subgradient of  at . If  is differentiable, then its only subgradient is the gradient vector  itself. It may happen that  is not a descent direction for  at . We therefore maintain a list  that keeps track of the lowest objective function value found so far, i.e.


下图来自:  http://www.stanford.edu/class/ee364b/notes/subgradients_notes.pdf
例2：SVM代价函数是hinge loss，在(1,0)除导数不存在，取1和1之间的数值，具体怎么取？Mingming Gong said好像这个pdf和 http://www.stanford.edu/class/ee364b/lectures/subgrad_method_slides.pdf，其中一个讲了。Mingming Gong asked tianyi, which is better, subgradient or smooth apprpximation?结论是不一定，subgradient解的是原问题，smooth不是解的原问题。一个相当于对梯度的近似，一个是对函数的近似，很难说哪个好。