Tuning Over-Relaxed ADMM
نویسندگان
چکیده
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program (SDP). In the case of over-relaxed Alternating Direction Method of Multipliers (ADMM), an explicit and closed form solution to this SDP was derived in our recent work [1]. The purpose of this paper is twofold. First, we summarize these results. Second, we explore one of its consequences which allows us to obtain general and simple formulas for optimal parameter selection. These results are valid for arbitrary strongly convex objective functions.
منابع مشابه
An Explicit Rate Bound for the Over-Relaxed ADMM
The framework of Integral Quadratic Constraints of Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). Followup work by Nishihara et al. (2015) applies this technique to the entire family of overrelaxed Alternating Direction Method of Multipliers (ADMM). Unfortunately, they only provide an e...
متن کاملAn augmented ADMM algorithm with application to the generalized lasso problem
In this article, we present a fast and stable algorithm for solving a class of optimization problems that arise in many statistical estimation procedures, such as sparse fused lasso over a graph, convex clustering, and trend filtering, among others. We propose a so-called augmented alternating direction methods of multipliers (ADMM) algorithm to solve this class of problems. Compared to a stand...
متن کاملFaster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions
Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art perform...
متن کاملPartial Convolution for Total Variation Deblurring and Denoising by New Linearized Alternating Direction Method of Multipliers with Extension Step
In this paper, we propose a partial convolution model for image delburring and denoising. We also devise a new linearized alternating direction method of multipliers (ADMM) with extension step. On one hand, the computation of its subproblem is dominated by several FFTs, hence its periteration cost is low, on the other hand, the relaxed parameter condition together with the extra extension step ...
متن کاملThe convergence rate of the proximal alternating direction method of multipliers with indefinite proximal regularization
The proximal alternating direction method of multipliers (P-ADMM) is an efficient first-order method for solving the separable convex minimization problems. Recently, He et al. have further studied the P-ADMM and relaxed the proximal regularization matrix of its second subproblem to be indefinite. This is especially significant in practical applications since the indefinite proximal matrix can ...
متن کامل