Paper Info
Title
A General Inertial Proximal Point Algorithm for Mixed Variational Inequality Problem.
Abstract
In this paper, we first propose a general inertial proximal point algorithm (PPA) for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, a convergence rate result is not known in the literature for inertial type PPAs. Under certain conditions, we are able to establish the global convergence and nonasymptotic O(1/k) convergence rate result (under a certain measure) of the proposed general inertial PPA. We then show that both the linearized augmented Lagrangian method (ALM) and the linearized alternating direction method of multipliers (ADMM) for structured convex optimization are applications of a general PPA, provided that the algorithmic parameters are properly chosen. Consequently, global convergence and convergence rate results of the linearized ALM and ADMM follow directly from results existing in the literature. In particular, by applying the proposed inertial PPA for mixed VI to structured convex optimization, we obtain inertial versions of the linearized ALM and ADMM whose global convergence is guaranteed. We also demonstrate the effect of the inertial extrapolation step via experimental results on the compressive principal component pursuit problem.
Year
DOI
Venue
2015
10.1137/140980910
SIAM JOURNAL ON OPTIMIZATION
Keywords
Field
DocType
inertial proximal point algorithm,mixed variational inequality,inertial linearized augmented Lagrangian method,inertial linearized alternating direction method of multipliers
Convergence (routing),Inertial frame of reference,Mathematical optimization,Proximal point,Algorithm,Augmented Lagrangian method,Rate of convergence,Convex optimization,Mathematics,Variational inequality
Journal
Volume
Issue
ISSN
25
4
1052-6234
Citations 
PageRank 
References 
2
0.36
0
Authors
3
Name
Order
Citations
PageRank
Caihua Chen11536.85
Shiqian Ma2106863.48
Junfeng Yang320.36