2024/11/14 by Tiantian Zhao, Zhao, Tiantian
Mathematics · #Advanced Optimization Algorithms Research #Differential Equations and Numerical Methods #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2411.09503
openalex publication_date 2024/11/14 · openalex created_date 2024/11/17 · openalex updated_date 2026/07/28
It has been shown that many first-order methods satisfy the perturbed Fenchel duality inequality, which yields a unified derivation of convergence. More first-order methods are discussed in this paper, e.g., dual averaging and bundle method. We show primal-dual convergence of them on convex optimization by proving the perturbed Fenchel duality property. We also propose a single-cut bundle method for saddle problem, and prove its convergence in a similar manner.