This work describes a framework for solving support vector machine with kernel (SVMK). Recently, it has been proved that the use of non-smooth loss function for supervised learning problem gives more efficient results [1]. This gives the idea of solving the SVMK problem based on hinge loss function. However, the hinge loss function is non-differentiable (we can’t use the standard optimization methods to minimize the empirical risk). To overcome this difficulty, a special smoothing technique for the hinge loss is proposed. Thus, the obtained smooth problem combined with Tikhonov regularization is solved using a stochastic gradient descent method. Finally, some numerical experiments on academic and real-life datasets are presented to show the efficiency of the proposed approach.

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