A P-ADMM for sparse quadratic kernel-free least squares semi-supervised support vector machine

In this paper, we propose a sparse quadratic kernel-free least squares semi-supervised support vector machine model by adding an L1 norm regularization term to the objective function and using the least squares method, which results in a nonconvex and nonsmooth quadratic programming problem. For computational considerations, we use the smoothing technique and consensus technique. Then we adopt the proximal alternating direction method of multipliers (P-ADMM) to solve it, as well as propose a strategy of parameter selection. Then we not only derive the convergence analysis of algorithm, but also estimate the convergence rate as o(1/k), where k is the number of iteration. This gives the best bound of P-ADMM known so far for nonconvex consensus problem. To demonstrate the efficiency of our model, we compare the proposed method with several state-of-the-art methods. The numerical results show that our model can achieve both better accuracy and sparsity.