Accelerating ADMM for efficient simulation and optimization

Zhang, Jie; Peng, Yue; Ouyang, Wenqing; Deng, Bailin

doi:10.1145/3355089.3356491

Cited by 51 publications

(79 citation statements)

References 93 publications

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“…Anderson acceleration was originally proposed in [37] for iterative solution of nonlinear integral equations, and has proved effective for accelerating fixed-point iterations [8], [38], [39], [40], [41], [42], [43], [44], [45]. In computer graphics, Anderson acceleration has been applied recently to accelerate local-global solvers [9] and ADMM solvers [46], [47].…”

Section: Related Workmentioning

confidence: 99%

“…Simply applying Anderson acceleration as explained in Section 4.1 is often not sufficient for fast convergence. It is known that Anderson acceleration can suffer from instability and stagnation even for linear problems [48], thus safeguarding steps are often necessary to improve its performance [9], [46], [56]. To this end, we follow the stabilization strategy proposed in [9]: we accept the accelerated value as the new iterate only if it decreases the target function (1) compared with the previous iterate; otherwise, we revert to the unaccelerated ICP iterate as the new iterate.…”

Section: Applying Anderson Acceleration To Icpmentioning

confidence: 99%

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Fast and Robust Iterative Closest Point

Zhang¹,

Yao²,

Deng³

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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115

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The Iterative Closest Point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to speed up its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.

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Section: Related Workmentioning

confidence: 99%

Section: Applying Anderson Acceleration To Icpmentioning

confidence: 99%

Fast and Robust Iterative Closest Point

Zhang¹,

Yao²,

Deng³

2021

IEEE Trans. Pattern Anal. Mach. Intell.

Self Cite

115

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“…Such equivalence enables us to interpret ADMM using its equivalent DR splitting form, which turns out to be a fixed‐point iteration for a linear transformation of the ADMM variables, with the same dimensionality as the dual variable y . As a result, we can apply Anderson acceleration to such alternative form of fixed‐point iteration, often with a much lower dimensionality than the fixed‐point iteration of ( x, y ) that is utilized in [ZPOD19] for the general case and with a lower computational overhead. Moreover, compared to the other acceleration techniques in [ZPOD19] based on reduced variables, our new approach has the same dimensionality for the fixed‐point iteration but requires a much weaker assumption on the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, we can apply Anderson acceleration to such alternative form of fixed‐point iteration, often with a much lower dimensionality than the fixed‐point iteration of ( x, y ) that is utilized in [ZPOD19] for the general case and with a lower computational overhead. Moreover, compared to the other acceleration techniques in [ZPOD19] based on reduced variables, our new approach has the same dimensionality for the fixed‐point iteration but requires a much weaker assumption on the optimization problem. To achieve stability of the Anderson acceleration, we propose two merit functions for determining whether an accelerated iterate can be accepted: 1) the DR envelope, with a strong guarantee for global convergence of the accelerated solver, and 2) the primal residual norm, which provides fewer theoretical guarantees but incurs lower computational overhead.…”

Section: Introductionmentioning

confidence: 99%

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Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting

Ouyang

Peng

Yao

et al. 2020

Computer Graphics Forum

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The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to converge to a solution of high-accuracy. 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. In this paper, we note that the equivalence between ADMM and Douglas-Rachford splitting reveals that ADMM is in fact a fixed-point iteration in a lower-dimensional space. By applying Anderson acceleration to such lower-dimensional fixed-point iteration, we obtain a more effective approach for accelerating ADMM. We analyze the convergence of the proposed acceleration method on nonconvex problems, and verify its effectiveness on a variety of computer graphics including geometry processing and physical simulation.

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Anderson‐accelerated polarization schemes for fast Fourier transform‐based computational homogenization

Wicht

Schneider

Böhlke

2021

Numerical Meth Engineering

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Classical solution methods in fast Fourier transform‐based computational micromechanics operate on, either, compatible strain fields or equilibrated stress fields. By contrast, polarization schemes are primal‐dual methods whose iterates are neither compatible nor equilibrated. Recently, it was demonstrated that polarization schemes may outperform the classical methods. Unfortunately, their computational power critically depends on a judicious choice of numerical parameters. In this work, we investigate the extension of polarization methods by Anderson acceleration and demonstrate that this combination leads to robust and fast general‐purpose solvers for computational micromechanics. We discuss the (theoretically) optimum parameter choice for polarization methods, describe how Anderson acceleration fits into the picture, and exhibit the characteristics of the newly designed methods for problems of industrial scale and interest.

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Accelerating ADMM for efficient simulation and optimization

Abstract: apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.

Cited by 51 publications

References 93 publications

Fast and Robust Iterative Closest Point

Fast and Robust Iterative Closest Point

Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting

Anderson‐accelerated polarization schemes for fast Fourier transform‐based computational homogenization

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