Splitting Method for Support Vector Machine in Reproducing Kernel Banach Space with a Lower Semi-continuous Loss Function

In this paper, the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework, where a lower semi-continuous loss function is utilized. They translate support vector machine in reproducing kernel Banach space with such a loss function to a finite-dimensional tensor optimization problem and propose a splitting method based on the alternating direction method of multipliers. Leveraging Kurdyka-Lojasiewicz property of the augmented Lagrangian function, the authors demonstrate that the sequence derived from this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subanalytic. Through several numerical examples, they illustrate the effectiveness of the proposed splitting algorithm.