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

Abstract

In this paper, we use the splitting method to solve support vector machine in reproducing kernel Banach space with lower semi-continuous loss function. We equivalently transfer support vector machines in reproducing kernel Banach space with lower semi-continuous loss function to a finite-dimensional tensor Optimization and propose the splitting method based on alternating direction method of multipliers. By Kurdyka-Lojasiewicz inequality, the iterative sequence obtained by this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subanalytic. Finally, several numerical performances demonstrate the effectiveness.