Splitting Method for Support Vector Machine with Lower Semi-continuous Loss

Time: 2023-11-23 11:23:00

    In this paper, we study the splitting method for support vector machine in reproducing kernel Hilbert space with lower semi-continuous loss function. We equivalently transfer support vector machine in reproducing kernel Hilbert space with lower semi-continuous loss function to a finite-dimensional Optimization and propose the splitting method based on alternating direction method of multipliers. If the loss function is lower semi-continuous and subanalytic, we use the Kurdyka-Lojasiewicz property of the augmented Lagrangian function to show that the iterative sequence induced by this splitting method globally converges to a stationary point. The numerical experiments also demonstrate the effectiveness of the splitting method.

References:

    1. Mingyu Mo and Qi Ye. Splitting Method for Support Vector Machine with Lower Semi-continuous Loss. Pacific Journal of Optimization. 2023, 19(4): 689-714. yokohamapublishers.jp/online2/pjov19-4.html