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

TL;DR

This paper introduces a splitting method based on the alternating direction method of multipliers to solve support vector machines in reproducing kernel Banach spaces with lower semi-continuous loss functions, ensuring global convergence and demonstrating effectiveness through numerical tests.

Contribution

It develops a novel splitting method for SVMs in Banach spaces with lower semi-continuous loss, transforming the problem into a finite-dimensional tensor optimization.

Findings

Global convergence of the iterative sequence to a stationary point.

Effective numerical performance demonstrated.

Applicable to lower semi-continuous and subanalytic loss functions.

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.