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Journal articles on the topic 'Semidefinite programming'

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Published: 4 June 2021
Last updated: 25 May 2024

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1

Helmberg, C. "Semidefinite programming." European Journal of Operational Research 137, no. 3 (March 2002): 461–82. http://dx.doi.org/10.1016/s0377-2217(01)00143-6.

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2

Vandenberghe, Lieven, and Stephen Boyd. "Semidefinite Programming." SIAM Review 38, no. 1 (March 1996): 49–95. http://dx.doi.org/10.1137/1038003.

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3

Overton, Michael, and Henry Wolkowicz. "Semidefinite programming." Mathematical Programming 77, no. 1 (April 1997): 105–9. http://dx.doi.org/10.1007/bf02614431.

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4

Yurtsever, Alp, Joel A. Tropp, Olivier Fercoq, Madeleine Udell, and Volkan Cevher. "Scalable Semidefinite Programming." SIAM Journal on Mathematics of Data Science 3, no. 1 (January 2021): 171–200. http://dx.doi.org/10.1137/19m1305045.

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5

Vandenberghe, Lieven, and Stephen Boyd. "Applications of semidefinite programming." Applied Numerical Mathematics 29, no. 3 (March 1999): 283–99. http://dx.doi.org/10.1016/s0168-9274(98)00098-1.

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6

Goldfarb, D., and K. Scheinberg. "On parametric semidefinite programming." Applied Numerical Mathematics 29, no. 3 (March 1999): 361–77. http://dx.doi.org/10.1016/s0168-9274(98)00102-0.

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7

Kalantari, Bahman. "Semidefinite programming and matrix scaling over the semidefinite cone." Linear Algebra and its Applications 375 (December 2003): 221–43. http://dx.doi.org/10.1016/s0024-3795(03)00664-5.

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8

Lidický, Bernard, and Florian Pfender. "Semidefinite Programming and Ramsey Numbers." SIAM Journal on Discrete Mathematics 35, no. 4 (January 2021): 2328–44. http://dx.doi.org/10.1137/18m1169473.

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9

Bofill, Walter Gómez, and Juan A. Gómez. "LINEAR AND NONLINEAR SEMIDEFINITE PROGRAMMING." Pesquisa Operacional 34, no. 3 (December 2014): 495–520. http://dx.doi.org/10.1590/0101-7438.2014.034.03.0495.

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10

Zhang, Tianyu, and Liwei Zhang. "Critical Multipliers in Semidefinite Programming." Asia-Pacific Journal of Operational Research 37, no. 04 (May 19, 2020): 2040012. http://dx.doi.org/10.1142/s0217595920400126.

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It was proved in Izmailov and Solodov (2014). Newton-Type Methods for Optimization and Variational Problems, Springer] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush–Kuhn–Thcker (KKT) system without any assumptions. This paper investigates whether this result still holds true for a (smooth) nonlinear semidefinite programming (SDP) problem. The answer is negative: the existence of noncritical multiplier does not imply the error bound condition for the KKT system without additional conditions, which is illustrated by an example. In this paper, we obtain characterizations, in terms of the problem data, the critical and noncritical multipliers for a SDP problem. We prove that, for the SDP problem, the noncriticality property can be derived from the error bound condition for the KKT system without any assumptions, and we give an example to show that the noncriticality does not imply the error bound for the KKT system. We propose a set of assumptions under which the error bound condition for the KKT system can be derived from the noncriticality property. a Finally, we establish a new error bound for [Formula: see text]-part, which is expressed by both perturbation and the multiplier estimation.
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11

d’Aspremont, Alexandre. "Subsampling Algorithms for Semidefinite Programming." Stochastic Systems 1, no. 2 (December 2011): 274–305. http://dx.doi.org/10.1287/10-ssy018.

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12

Zhang, Qinghong, Gang Chen, and Ting Zhang. "Duality formulations in semidefinite programming." Journal of Industrial & Management Optimization 6, no. 4 (2010): 881–93. http://dx.doi.org/10.3934/jimo.2010.6.881.

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13

Schellewald, C., and C. Schnörr. "Subgraph Matching with Semidefinite Programming." Electronic Notes in Discrete Mathematics 12 (March 2003): 279–89. http://dx.doi.org/10.1016/s1571-0653(04)00493-7.

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14

Malick, Jérôme, Janez Povh, Franz Rendl, and Angelika Wiegele. "Regularization Methods for Semidefinite Programming." SIAM Journal on Optimization 20, no. 1 (January 2009): 336–56. http://dx.doi.org/10.1137/070704575.

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15

Penot, Jean-Paul. "Optimality Conditions in Semidefinite Programming." Numerical Functional Analysis and Optimization 35, no. 7-9 (July 3, 2014): 1174–96. http://dx.doi.org/10.1080/01630563.2014.895763.

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16

Rendl, Franz. "Semidefinite programming and combinatorial optimization." Applied Numerical Mathematics 29, no. 3 (March 1999): 255–81. http://dx.doi.org/10.1016/s0168-9274(98)00097-x.

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17

Thake, A. J., P. J. McLellan, and J. F. Forbes. "Controller Approximation Using Semidefinite Programming." Industrial & Engineering Chemistry Research 38, no. 7 (July 1999): 2699–708. http://dx.doi.org/10.1021/ie980536h.

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18

Yuan, Ganzhao, Zhenjie Zhang, Bernard Ghanem, and Zhifeng Hao. "Low-rank quadratic semidefinite programming." Neurocomputing 106 (April 2013): 51–60. http://dx.doi.org/10.1016/j.neucom.2012.10.014.

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19

Shapiro, Alexander. "Statistical inference of semidefinite programming." Mathematical Programming 174, no. 1-2 (February 28, 2018): 77–97. http://dx.doi.org/10.1007/s10107-018-1250-z.

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20

Bogaerts, Mathieu, and Peter Dukes. "Semidefinite programming for permutation codes." Discrete Mathematics 326 (July 2014): 34–43. http://dx.doi.org/10.1016/j.disc.2014.03.002.

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21

Ramana, Motakuri V., Levent Tunçel, and Henry Wolkowicz. "Strong Duality for Semidefinite Programming." SIAM Journal on Optimization 7, no. 3 (August 1997): 641–62. http://dx.doi.org/10.1137/s1052623495288350.

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22

Zhang, Qinghong. "Embedding methods for semidefinite programming." Optimization Methods and Software 27, no. 3 (June 2012): 461–82. http://dx.doi.org/10.1080/10556788.2010.534475.

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23

Lovász, László. "Integer sequences and semidefinite programming." Publicationes Mathematicae Debrecen 56, no. 3-4 (April 1, 2000): 475–79. http://dx.doi.org/10.5486/pmd.2000.2362.

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24

Goemans, Michel X. "Semidefinite programming in combinatorial optimization." Mathematical Programming 79, no. 1-3 (October 1997): 143–61. http://dx.doi.org/10.1007/bf02614315.

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25

Lasserre, Jean B. "Semidefinite Programming vs. LP Relaxations for Polynomial Programming." Mathematics of Operations Research 27, no. 2 (May 2002): 347–60. http://dx.doi.org/10.1287/moor.27.2.347.322.

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26

Deák, István, Imre Pólik, András Prékopa, and Tamás Terlaky. "Convex approximations in stochastic programming by semidefinite programming." Annals of Operations Research 200, no. 1 (October 1, 2011): 171–82. http://dx.doi.org/10.1007/s10479-011-0986-0.

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27

Zhao, Qi, and Zhongwen Chen. "An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming." Asia-Pacific Journal of Operational Research 35, no. 03 (May 31, 2018): 1850009. http://dx.doi.org/10.1142/s0217595918500094.

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A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The [Formula: see text] exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorithm with the second-order correction step and prove that the fast local superlinear convergence can be obtained under the strict complementarity and the second-order sufficient condition with the sigma term. Finally, some numerical experiments are given to show the effectiveness of the algorithm.
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28

Chen, Yannan, Yuhong Dai, Deren Han, and Wenyu Sun. "Positive Semidefinite Generalized Diffusion Tensor Imaging via Quadratic Semidefinite Programming." SIAM Journal on Imaging Sciences 6, no. 3 (January 2013): 1531–52. http://dx.doi.org/10.1137/110843526.

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29

Burer, Samuel. "Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices." SIAM Journal on Optimization 14, no. 1 (January 2003): 139–72. http://dx.doi.org/10.1137/s105262340240851x.

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30

Vo, Cong, Masakazu Muramatsu, and Masakazu Kojima. "EQUALITY BASED CONTRACTION OF SEMIDEFINITE PROGRAMMING RELAXATIONS IN POLYNOMIAL OPTIMIZATION." Journal of the Operations Research Society of Japan 51, no. 1 (2008): 111–25. http://dx.doi.org/10.15807/jorsj.51.111.

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31

Wang, Po-Wei, and J. Zico Kolter. "Low-Rank Semidefinite Programming for the MAX2SAT Problem." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1641–49. http://dx.doi.org/10.1609/aaai.v33i01.33011641.

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This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.
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32

Ding, Ke-wei. "Distributionally Robust Joint Chance Constrained Problem under Moment Uncertainty." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/487178.

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We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which can be reformulated by a semidefinite programming. Then the chance constrained problem can be presented as semidefinite programming. We also find that the approximation for robust joint chance constraints has an equivalent individual quadratic approximation form.
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33

Wu, Jia, Yi Zhang, Liwei Zhang, and Yue Lu. "A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem." Asia-Pacific Journal of Operational Research 33, no. 04 (August 2016): 1650025. http://dx.doi.org/10.1142/s0217595916500251.

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This paper is devoted to the study of solving method for a type of inverse linear semidefinite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is actually a nonsmooth DC programming problem which can be solved by a sequential convex program approach. Convergence analysis of the penalty models and the sequential convex program approach are shown. Numerical results are reported to demonstrate the efficiency of our approach.
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34

Fushiki, Tadayoshi. "Estimation of Positive Semidefinite Correlation Matrices by Using Convex Quadratic Semidefinite Programming." Neural Computation 21, no. 7 (July 2009): 2028–48. http://dx.doi.org/10.1162/neco.2009.04-08-765.

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The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume an approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.
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35

Gvozdenović, Nebojša, Monique Laurent, and Frank Vallentin. "Block-diagonal semidefinite programming hierarchies for 0/1 programming." Operations Research Letters 37, no. 1 (January 2009): 27–31. http://dx.doi.org/10.1016/j.orl.2008.10.003.

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36

Blanco, Victor, Justo Puerto, and Safae El Haj Ben Ali. "A Semidefinite Programming approach for solving Multiobjective Linear Programming." Journal of Global Optimization 58, no. 3 (March 21, 2013): 465–80. http://dx.doi.org/10.1007/s10898-013-0056-z.

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37

Fu, Taoran. "On Doubly Positive Semidefinite Programming Relaxations." Journal of Computational Mathematics 36, no. 3 (June 2018): 391–403. http://dx.doi.org/10.4208/jcm.1708-m2017-0130.

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38

Rontsis, Nikitas, Paul Goulart, and Yuji Nakatsukasa. "Efficient Semidefinite Programming with Approximate ADMM." Journal of Optimization Theory and Applications 192, no. 1 (November 27, 2021): 292–320. http://dx.doi.org/10.1007/s10957-021-01971-3.

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AbstractTenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting approximately to the Semidefinite cone. Instead of computing the projections via “exact” eigendecompositions that scale cubically with the matrix size and cannot be warm-started, we suggest using state-of-the-art factorization-free, approximate eigensolvers, thus achieving almost quadratic scaling and the crucial ability of warm-starting. Using a recent result from Goulart et al. (Linear Algebra Appl 594:177–192, 2020. https://doi.org/10.1016/j.laa.2020.02.014), we are able to circumvent the numerical instability of the eigendecomposition and thus maintain tight control on the projection accuracy. This in turn guarantees convergence, either to a solution or a certificate of infeasibility, of the ADMM algorithm. To achieve this, we extend recent results from Banjac et al. (J Optim Theory Appl 183(2):490–519, 2019. https://doi.org/10.1007/s10957-019-01575-y) to prove that reliable infeasibility detection can be performed with ADMM even in the presence of approximation errors. In all of the considered problems of SDPLIB that “exact” ADMM can solve in a few thousand iterations, our approach brings a significant, up to 20x, speedup without a noticeable increase in ADMM’s iterations.
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39

Hauenstein, Jonathan D., Alan C. Liddell, Sanesha McPherson, and Yi Zhang. "Numerical algebraic geometry and semidefinite programming." Results in Applied Mathematics 11 (August 2021): 100166. http://dx.doi.org/10.1016/j.rinam.2021.100166.

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40

Mullan, Michael, and Emanuel Knill. "Improving quantum clocks via semidefinite programming." Quantum Information and Computation 12, no. 7&8 (July 2012): 553–74. http://dx.doi.org/10.26421/qic12.7-8-2.

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The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary operations and measurements. Here, we take advantage of these choices and present a numerical technique designed to increase the accuracy of these clocks. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after an interrogation step; we do not optimize over successive interrogations or the probe times. We consider arbitrary prior frequency knowledge and compare clocks with varying numbers of ions and queries interlaced with unitary control. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small.
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41

Vandenberghe, Lieven, Stephen Boyd, and Katherine Comanor. "Generalized Chebyshev Bounds via Semidefinite Programming." SIAM Review 49, no. 1 (January 2007): 52–64. http://dx.doi.org/10.1137/s0036144504440543.

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42

Comanor, Katherine, Lieven Vandenberghe, and Stephen Boyd. "SEMIDEFINITE PROGRAMMING AND MULTIVARIATE CHEBYSHEV BOUNDS." IFAC Proceedings Volumes 39, no. 9 (2006): 597–601. http://dx.doi.org/10.3182/20060705-3-fr-2907.00102.

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43

Karger, David, Rajeev Motwani, and Madhu Sudan. "Approximate graph coloring by semidefinite programming." Journal of the ACM 45, no. 2 (March 1998): 246–65. http://dx.doi.org/10.1145/274787.274791.

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44

Li, Hongying, Marc C. Robini, Feng Yang, Isabelle Magnin, and Yuemin Zhu. "Cardiac Fiber Unfolding by Semidefinite Programming." IEEE Transactions on Biomedical Engineering 62, no. 2 (February 2015): 582–92. http://dx.doi.org/10.1109/tbme.2014.2360797.

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45

Zhang, Shuzhong, and Yongwei Huang. "Complex Quadratic Optimization and Semidefinite Programming." SIAM Journal on Optimization 16, no. 3 (January 2006): 871–90. http://dx.doi.org/10.1137/04061341x.

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46

Musin, O. R. "Bounds for codes by semidefinite programming." Proceedings of the Steklov Institute of Mathematics 263, no. 1 (December 2008): 134–49. http://dx.doi.org/10.1134/s0081543808040111.

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47

Yang, Shouhong. "Semidefinite programming via image space analysis." Journal of Industrial and Management Optimization 12, no. 4 (January 2016): 1187–97. http://dx.doi.org/10.3934/jimo.2016.12.1187.

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48

Anstreicher, Kurt M. "The Volumetric Barrier for Semidefinite Programming." Mathematics of Operations Research 25, no. 3 (August 2000): 365–80. http://dx.doi.org/10.1287/moor.25.3.365.12212.

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49

Fares, B., D. Noll, and P. Apkarian. "Robust Control via Sequential Semidefinite Programming." SIAM Journal on Control and Optimization 40, no. 6 (January 2002): 1791–820. http://dx.doi.org/10.1137/s0363012900373483.

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50

Kovalsky, Shahar Z., Noam Aigerman, Ronen Basri, and Yaron Lipman. "Controlling singular values with semidefinite programming." ACM Transactions on Graphics 33, no. 4 (July 27, 2014): 1–13. http://dx.doi.org/10.1145/2601097.2601142.

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