Numerical solution of the generalized-loss SVM formulation

Determine a numerical solution for the generalized-loss support vector machine optimization problems whose dual formulations additionally require the primal slack variables.

Background

For the proposed SVM loss, the authors derive a dual formulation in which the admissible bounds on the dual variables depend on the slack variables. Consequently, the dual problem cannot be solved directly using the usual kernel SVM machinery. The paper addresses the primal SVM problem experimentally with Particle Swarm Optimization, but the stated difficulty concerning a numerical solution of the emerging formulation remains unresolved in the cited passage.