Many experts have designed algorithms for the -minimization model and discussed their convergence. However, at present, convergence to a stable point, as defined in Definition of this paper, is only assured for convergent subsequences. On the other hand, the literature on the difference of convex functions algorithm (DCA) is extensive, but proving the convergence of the DCA algorithm requires the use of the Kurdyka–Lojasiewicz (KL) property. In this paper, drawing on the ideas of the DCA, we propose a novel algorithm whose entire sequence converges to a stable point. We establish this result without relying on the KL property. Additionally, we prove that the number of local minimum points of the -minimization model is finite. Leveraging this result, we demonstrate that when the initial point is in proximal to a minimum point of the objective function, the algorithm converges to one of these minimum points. This paper provides the necessary and sufficient conditions for local minimum point of -minimization. Furthermore, we establish the convergence of the subalgorithm utilized to solve an optimization problem within the main algorithm. Finally, our experiments demonstrate that the algorithm proposed in this paper outperforms several other existing algorithms.
