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GMRES-Accelerated ADMM for Quadratic Objectives [article]

Richard Y. Zhang, Jacob K. White
2018 arXiv   pre-print
We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which  ...  Within this context, the ADMM update equations are linear, the iterates are confined within a Krylov subspace, and the General Minimum RESidual (GMRES) algorithm is optimal in its ability to accelerate  ...  Serrallés for proofreading an early draft, and for assisting with the numerical results; László Miklós Lovász for discussions on random matrix theory that led to Section 5.2.  ... 
arXiv:1601.06200v5 fatcat:llf732peqjgjlcbadoovxu3uou

Scalable Preconditioning of Block-Structured Linear Algebra Systems using ADMM [article]

Jose S. Rodriguez, Carl D. Laird, Victor M. Zavala
2019 arXiv   pre-print
We find that ADMM-GMRES is nearly an order of magnitude faster than Schur complement decomposition.  ...  Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of multipliers (ADMM).  ...  Heuristic approaches have also been proposed to select ρ at every ADMM iteration with the objective of accelerating convergence [36] .  ... 
arXiv:1904.11003v1 fatcat:fis24khdjja3xl5f252ywr6nse

Parameter Insensitivity in ADMM-Preconditioned Solution of Saddle-Point Problems [article]

Richard Y. Zhang, Jacob K. White
2016 arXiv   pre-print
We consider the solution of linear saddle-point problems, using the alternating direction method-of-multipliers (ADMM) as a preconditioner for the generalized minimum residual method (GMRES).  ...  We show, using theoretical bounds and empirical results, that ADMM is made remarkably insensitive to the parameter choice with Krylov subspace acceleration.  ...  Accelerating Convergence using GMRES. In the context of quadratic objectives, the convergence of ADMM can be accelerated by GMRES in a largely plug-and-play manner.  ... 
arXiv:1602.02135v3 fatcat:gsevp3i66fdxbpiczsn5k5ts5i

On the Asymptotic Linear Convergence Speed of Anderson Acceleration Applied to ADMM [article]

Dawei Wang, Yunhui He, Hans De Sterck
2020 arXiv   pre-print
Empirical results show that Anderson acceleration (AA) can be a powerful mechanism to improve the asymptotic linear convergence speed of the Alternating Direction Method of Multipliers (ADMM) when ADMM  ...  In this paper we explain and quantify this improvement in linear asymptotic convergence speed for the special case of a stationary version of AA applied to ADMM.  ...  A GMRES-accelerated ADMM is discussed in [27] for a quadratic objective, for which the ADMM iteration is linear.  ... 
arXiv:2007.02916v3 fatcat:4cca6gkk5zcv5gvzxhwgnd4uuq

Accelerating ADMM for Efficient Simulation and Optimization [article]

Juyong Zhang, Yue Peng, Wenqing Ouyang, Bailin Deng
2019 arXiv   pre-print
In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations.  ...  Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization.  ...  Also included in the comparison is the GMRES acceleration for ADMM proposed in [Zhang and White 2018] , which is designed specifically for strongly convex quadratic problems.  ... 
arXiv:1909.00470v1 fatcat:llu4vly6bvfbfpswvdpzulkkqi

A Semismooth Newton Method for Fast, Generic Convex Programming [article]

Alnur Ali, Eric Wong, J. Zico Kolter
2017 arXiv   pre-print
We introduce Newton-ADMM, a method for fast conic optimization.  ...  We demonstrate theoretically, by extending the theory of semismooth operators, that Newton-ADMM converges rapidly (i.e., quadratically) to a solution; empirically, Newton-ADMM is significantly faster than  ...  We thank Po-Wei Wang and the referees for a careful proof-reading.  ... 
arXiv:1705.00772v2 fatcat:7m5ajqubhbgvvhazxnzaoskpfq

Solving Variational Inequalities and Cone Complementarity Problems in Non‐Smooth Dynamics using the Alternating Direction Method of Multipliers

Alessandro Tasora, Dario Mangoni, Simone Benatti, Rinaldo Garziera
2021 International Journal for Numerical Methods in Engineering  
For the special case of hard frictional contacts, the method solves a second order cone complementarity problem.  ...  We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives.  ...  In Reference 35 the Nesterov acceleration method has been proposed for problems where at least one of the two objectives is quadratic, and under the assumption that both objectives are strongly convex;  ... 
doi:10.1002/nme.6693 fatcat:o4hs7hwhofbt7l2fljlggu5xqm

Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting [article]

Wenqing Ouyang and Yue Peng and Yuxin Yao and Juyong Zhang and Bailin Deng
2020 arXiv   pre-print
By applying Anderson acceleration to such lower-dimensional fixed-point iteration, we obtain a more effective approach for accelerating ADMM.  ...  Previously, Anderson acceleration has been applied to ADMM, by treating it as a fixed-point iteration for the concatenation of the dual variables and a subset of the primal variables.  ...  Acknowledgements The authors thank Andre Milzarek for proofreading the paper and providing valuable comments. The target model in Figure 4  ... 
arXiv:2006.14539v2 fatcat:wci4nih6ybfmpl3ko376iyuyqi

Compressive Conjugate Directions: Linear Theory [article]

Musa Maharramov, Stewart A. Levin
2016 arXiv   pre-print
algorithm across multiple iterations of the ADMM.  ...  We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve L_1/total-variation (TV) regularization.  ...  By accumulating and reusing information on the geometry of the intermediate quadratic objective function (4.4), the method requires only one application of the operator A and its adjoint per ADMM iteration  ... 
arXiv:1602.06111v2 fatcat:a53trqgs75bhjmagfxyd45acya

An FE-dABCD algorithm for elliptic optimal control problems with constraints on the gradient of the state and control [article]

Zixuan Chen, Xiaoliang Song, Bo Yu, Xiaotong Chen
2018 arXiv   pre-print
For the smooth subproblem, we use the generalized minimal residual (GMRES) method with preconditioner to slove it.  ...  The entire algorithm framework is called finite element duality-based inexact majorized accelerating block coordinate descent (FE-dABCD) algorithm.  ...  Long Chen very much for the contribution of the FEM package iFEM [7] in Matlab.  ... 
arXiv:1810.01923v1 fatcat:qynsiis2nrbvdanlrnkp23ynee

PRESAS: Block-Structured Preconditioning of Iterative Solvers within a Primal Active-Set Method for fast MPC [article]

Rien Quirynen, Stefano Di Cairano
2020 arXiv   pre-print
Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant.  ...  This paper proposes a primal active-set strategy (PRESAS) for the efficient solution of such block-sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration  ...  For example, this is observed for the computation time of the ADMM solver.  ... 
arXiv:1912.02122v2 fatcat:bvdj3eglhjaijnjokpbgapbhxy

On the Asymptotic Linear Convergence Speed of Anderson Acceleration, Nesterov Acceleration, and Nonlinear GMRES [article]

Hans De Sterck, Yunhui He
2020 arXiv   pre-print
We consider nonlinear convergence acceleration methods for fixed-point iteration x_k+1=q(x_k), including Anderson acceleration (AA), nonlinear GMRES (NGMRES), and Nesterov-type acceleration (corresponding  ...  Since AA and NGMRES are equivalent to GMRES in the linear case, one may expect the GMRES convergence factors to be relevant for AA and NGMRES as x_k → x^*.  ...  objectives.  ... 
arXiv:2007.01996v4 fatcat:czyfj7a56ngithkmz2jf6ib2z4

An efficient duality-based approach for PDE-constrained sparse optimization [article]

Xiaoliang Song, Bo Chen, Bo Yu
2017 arXiv   pre-print
The design of this method combines an inexact 2-block majorized ABCD and the recent advances in the inexact symmetric Gauss-Seidel (sGS) technique for solving a multi-block convex composite quadratic programming  ...  whose objective contains a nonsmooth term involving only the first block.  ...  Long Chen for the FEM package iFEM [43] in Matlab.  ... 
arXiv:1708.09094v1 fatcat:jhilts5cdjeyrgkookd2djoiuq

Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations [article]

Spyridon Pougkakiotis, John W. Pearson, Santolo Leveque, Jacek Gondzio
2020 arXiv   pre-print
We develop an Alternating Direction Method of Multipliers (ADMM) framework, which uses preconditioned Krylov subspace solvers for the resulting sub-problems.  ...  In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control  ...  We note that while various potential acceleration strategies for ADMMs have been studied in the literature (see for example [5, 36] ), the focus of the paper is to illustrate the viability of the proposed  ... 
arXiv:1907.13428v4 fatcat:5ytqsreurbedbjgqu2pkunucem

Implementation of the ADMM to Parabolic Optimal Control Problems with Control Constraints and Beyond [article]

Yongcun Song, Xiaoming Yuan, Hangrui Yue
2020 arXiv   pre-print
At each iteration of the ADMM, the main computation is for solving an unconstrained parabolic optimal control problem.  ...  Efficiency of this ADMM implementation is promisingly validated by preliminary numerical results.  ...  Figure 1 : 1 Residuals (left) and objective functional values (right) with respect to outer ADMM iterations for Example 1.  ... 
arXiv:2005.01582v1 fatcat:oprmrk3bjranzaf4s7hqb3tlky
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