L2-SVM: Dependence on the regularization parameter

The goal of this paper is to announce some results dealing with mathematical properties of so-called L2 Soft-Margin Support Vector Machines (L2-SVMs) for data classification. Their dual formulations build a family of quadratic programming problems depending on one regularization parameter. The dependence of the solution on this parameter is examined. Such properties as continuity, differentiability, monotony and convexity are investigated. It is shown that the solution and the objective value of the Hard Margin SVM allow estimating the slack variables of the L2-SVMs. The asymptotic behavior of the solutions of the primal problems in the inseparable case was investigated. An ancillary dual problem is used as investigation tool. It is in reality a dual formulation of a quasi identical L2-SVM primal.