Proximal Regularization for the Saddle Point Gradient Dynamics

• 成果类型: Article
• 署名作者: Goldsztajn, Diego; Paganini, Fernando
• 署名单位: Eindhoven University of Technology; University ORT Uruguay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3045124
• 发表日期: 2021
• 页码: 4385-4392
• 关键词: Optimization; CONVERGENCE; control theory; asymptotic stability; resource management; Convex functions; trajectory; Convex Optimization; proximal method; saddle point dynamics

摘要

This article concerns the solution of a convex optimization problem through the saddle point gradient dynamics. Instead of using the standard Lagrangian as is classical in this method, we consider a regularized Lagrangian obtained through a proximal minimization step. We show that, without assumptions of smoothness or strict convexity in the original problem, the regularized Lagrangian is smooth and leads to globally convergent saddle point dynamics. The method is demonstrated through an application to resource allocation in cloud computing.