Soft Quadratic Support Vector Machine With L_0/1 Loss Function

Support vector machine(SVM)have been widely used in machine learning,statistics,pattern recognition and other fields,so it has important application value for the exploration of such problems.SVM as a binary classification model,when the dataset is nonlinearly divisible,the kernel function is introduced to make the data linearly separable,but the use of kernel function often requires huge computation.In order to overcome this difficulty,the soft margin quadratic support vector machine model(QSVM)via the L0/1 loss function will be studied in this paper,and since the objective function studied in this paper is separable,the alternating direction multiplier method(ADMM)can be used to solve the optimization problem.Under reasonable assumptions,it is proved that the augmented Lagrangian function of the problem satisfies the Kurdyka-Lojasiewicz property,and then proves the convergence of the algorithm.