Passivity-based generalization of primal-dual dynamics for non-strictly convex cost functions

作     者：Yamashita, Shunya Hatanaka, Takeshi Yamauchi, Junya Fujita, Masayuki 

作者机构：Department of Systems and Control Engineering School of Engineering Tokyo Institute of Technology S5-26 2-12-1 Ookayama Meguro-ku Tokyo Japan Division of Electrical Electronic and Information Engineering Graduate School of Engineering Osaka University 2-1 Yamadaoka Osaka Suita 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2018年

核心收录：

主　　题：Convex optimization 

摘      要：In this paper, we revisit primal-dual dynamics for convex optimization and present a generalization of the dynamics based on the concept of passivity. It is then proved that supplying a stable zero to one of the integrators in the dynamics allows one to eliminate the assumption of strict convexity on the cost function based on the passivity paradigm together with the invariance principle for Carathéodory systems. We then show that the present algorithm is also a generalization of existing augmented Lagrangian-based primal-dual dynamics, and discuss the benefit of the present generalization in terms of noise reduction and convergence speed. Copyright © 2018, The Authors. All rights reserved.