Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting

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

doi:10.1111/cgf.14081

Cited by 24 publications

(11 citation statements)

References 77 publications

(179 reference statements)

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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%

Fast and Robust Iterative Closest Point

Zhang¹,

Yao²,

Deng³

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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116

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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%

Fast and Robust Iterative Closest Point

Zhang¹,

Yao²,

Deng³

2021

IEEE Trans. Pattern Anal. Mach. Intell.

Self Cite

116

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“…Proximal algorithms [PB14] provide a way around this restriction, in which energy or constraint evaluations are broken down into smaller, easier to solve proximal operators that can be evaluated even at infeasible points. The alternating direction method of multipliers (ADMM) is a proximal algorithm that has gained popularity in the computer graphics community [BOFN18,ZPOD19,LJ19,FLGJ19,OPY∗20]. ADMM‐PD [OBLN17] in particular has several attractive features, including support for arbitrary nonlinear deformation energies with or without infinite energy barriers, and fast iterations using a prefactored linear solve.…”

Section: Related Workmentioning

confidence: 99%

Globally Injective Geometry Optimization with Non‐Injective Steps

Overby

Kaufman

Narain

2021

Computer Graphics Forum

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We present a method to minimize distortion and compute globally injective mappings from non‐injective initialization Many approaches for distortion minimization subject to injectivity constraints require an injective initialization and feasible intermediate states. However, it is often the case that injective initializers are not readily available, and many distortion energies of interest have barrier terms that stall global progress. The alternating direction method of multipliers (ADMM) has recently gained traction in graphics due to its efficiency and generality. In this work we explore how to endow ADMM with global injectivity while retaining the ability to traverse non‐injective iterates. We develop an iterated coupled‐solver approach that evolves two solution states in tandem. Our primary solver rapidly drives down energy to a nearly injective state using a dynamic set of efficiently enforceable inversion and overlap constraints. Then, a secondary solver corrects the state, herding the solution closer to feasibility. The resulting method not only compares well to previous work, but can also resolve overlap with free boundaries.

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“…Thus, by relieving the user of the daunting task of identifying the optimum numerical parameters, the Anderson‐accelerated polarization scheme turns into a general‐purpose solver for FFT‐based computational micromechanics. We wish to draw the reader's attention to recent applications 50,59,60 of Anderson acceleration to operator‐splitting methods, which motivated the present work.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, Shantraj et al 61 consider the deformation gradient and a rescaled polarization field as iterates of their algorithm. However, a recent study by Ouyang et al 60 demonstrates that it is preferable in terms of iteration counts and run‐time to restrict Anderson acceleration to the lower‐dimensional fixed‐point iteration of the polarization. In the context of FFT‐based micromechanics, this corresponds to accelerating the (damped) Eyre–Milton iteration, which is the approach we follow in this study.…”

Section: Introductionmentioning

confidence: 99%

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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Anderson Acceleration for Nonconvex ADMM Based on Douglas‐Rachford Splitting

Cited by 24 publications

References 77 publications

Fast and Robust Iterative Closest Point

Fast and Robust Iterative Closest Point

Globally Injective Geometry Optimization with Non‐Injective Steps

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

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