2021/03/11 by Hao Luo, Luo, Hao · 2 citations
Computer Science · Engineering · Mathematics · #37M99 #37N40 #65K05 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2103.06636
openalex publication_date 2021/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our primal-dual flow is proved to possess the exponential decay property, in terms of a tailored Lyapunov function. Then two primal-dual methods are obtained from numerical discretizations of the continuous model, and global nonergodic linear convergence rate is established via a discrete Lyapunov function. Instead of solving the subproblem of the primal variable, we apply the semi-smooth Newton iteration to the subproblem with respect to the multiplier, provided that there are some additional properties such as semi-smoothness and sparsity. Especially, numerical tests on the linearly constrained l1-l2 minimization and the total-variation based image denoising model have been provided.