- A general inertial proximal point algorithm for mixed variational inequality problem caihua chen(chchennju.edu.cn) shiqian ma(sqmase.cuhk.edu.cn) junfeng yang(jfyangnju.edu.cn) Abstract: In this paper, we first propose a general inertial \emph{proximal point algorithm} (PPA) for the mixed \emph{variational inequality} (VI) problem. Based on our knowledge, without stronger assumptions, 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 certain measure) of the proposed general inertial PPA. We then show that both the linearized \emph{augmented Lagrangian method} (ALM) and the linearized \emph{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 are guaranteed. We also demonstrate the effect of the inertial extrapolation step via experimental results on the compressive principal component pursuit problem. Keywords: inertial proximal point algorithm, mixed variational inequality, inertial linearized augmented Lagrangian method, inertial linearized alternating direction method of multipliers. Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: SIAM Journal on Optimization, to appear. Download: [PDF]Entry Submitted: 08/24/2015Entry Accepted: 08/24/2015Entry Last Modified: 08/24/2015Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.