2025/07/04 by Ye, Yuge, Li, Qingna
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2507.03566
In this paper, we propose a globally convergent Newton type method to solve ℓ0 regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix of the original problem is a block upper triangular matrix. To reduce the computational burden, our method only requires the calculation of the block diagonal. We also introduced regularization to overcome matrix singularity. Although we only use the block-diagonal part of the Jacobian matrix, our algorithm still maintains global convergence and achieves a local quadratic convergence rate. Numerical results demonstrate the efficiency of our method.