Publications

Journal Publications

1. Amir Beck and Marc Teboulle, Global optimality conditions for quadratic optimization problems with binary constraints , SIAM J. Optim. 11 (2000), no. 1, 179--188. 

2. Amir Beck and Marc Teboulle, A probabilistic result for the max-cut problem on random graphs , Oper. Res. Lett. 27 (2000), no. 5, 209--214. 

3. Amir Beck and Marc Teboulle, Convergence rate analysis and error bounds for projection algorithms in convex feasibility problems , Optim. Methods Softw. 18 (2003), no. 4, 377--394. 

4. Amir Beck and Marc Teboulle, Mirror descent and nonlinear projected subgradient methods for convex optimization , Oper. Res. Lett. 31 (2003), no. 3, 167--175. 

5. Amir Beck and Marc Teboulle, A conditional gradient method with linear rate of convergence for solving convex linear systems, Math. Methods Oper. Res. 59 (2004), no. 2, 235--247.

6. Amir Beck and Aharon Ben-Tal, A Global Solution for the Structured Total Least Squares Problem with Block Circulant Matrices, SIAM J. Matrix Anal. Appl. 27(1): 238-255. 

7. Amir Beck, Aharon ben-Tal and Yonina C. Eldar Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems affected by Model and Noise Uncertainties , Math. Program. 107, 155-187 (2006). 

8. Amir Beck, Aharon Ben-Tal and Marc Teboulle Finding a Global Optimal Solution for a Quadratically Constrained Fractional Quadratic Problem with Applications to the Regularized Total Least Squares , SIAM J. Matrix Anal. Appl. 28(2):425-445,2006.

9. Ami Wiesel, Yonina C. Eldar and Amir Beck, Maximum likelihood estimation in linear models with a Gaussian model matrix,IEEE Signal Processing Letters 13(5): 292-295, 2006.

10. Amir Beck and Marc Teboulle A linearly Convergent Dual-Based Gradient Projection Algorithm for Quadratically Constrained Convex Minimization , Math. Oper. Res., vol. 31 (2), Feb. 2006. 

11. Amir Beck and Aharon Ben-Tal On the Solution of the Tikhonov Regularization of the Total Least Squares , SIAM J. Optimization, 17(1): 98-118 (2006).

12. Amir Beck and Yonina C. Eldar Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints SIAM J. Optimization, 17 (3), 844-860 (2006). 

13. Amir Beck, Quadratic Matrix Programming , SIAM J. Optimization 17 (4), 1224-1238 (2006).

14. Amir Beck and Yonina C. Eldar, Doubly Constrained Robust Capon Beamformer with Ellipsoidal Uncertainty Sets, IEEE Trans. Signal Proc. 55 (2), 753-758 (2007). 

15. Amir Beck, The Matrix-Restricted Total Least Squares Problem, Signal Processing 87 (10), 2303-2312 (2007). 

16. Amir Beck, On the Convexity of a Class of Quadratic Mappings and its Application to the Problem of Finding the Smallest Ball Enclosing a Given Intersection of Ball , Journal of Global Optimization, 39(1), 113--126, 2007. 

17. Amir Beck and Yonina C. Eldar, Regularization in Regression with Bounded Noise: A Chebyshev Center Approach, SIAM J. Matrix Anal. Appl. 29 (2), 606-625 (2007). 

18. Amir Beck, Yonina C. Eldar and Aharon Ben-Tal Mean-Squared Error Estimation of Multichannel Signals, SIAM J. Matrix Anal. Appl. 29 (3), 712-730 (2007).

19. Pakize Taylan, Gerhard-Wilhelm Weber and Amir Beck, New Approaches to Regression by Generalized Additive Models and Continuous Optimization for Modern Applications in Finance, Science and Technology, Optimization, 56, nos. 5 & 6 (2007), 675--698. 

20. Amir Beck, Petre Stoica and Jian Li, Exact and Approximate Solutions of Source Localization Problems, IEEE Trans. Signal Proc, vol 56, no. 5, May 2008. 

21. Yonina Eldar, Amir Beck and Marc Teboulle, A Minimax Chebyshev Estimator for Bounded Error Estimation, IEEE Trans. Signal Proc, Vol. 56, No. 4, April 2008. 

22. Amir Beck, Aharon Ben-Tal and Christian Kanzow, "A Fast Method for Finding the Global Solution of the Regularized Structured Total Least Squares Problem for Image Deblurring " SIAM Journal on Matrix Analysis and Applications 30 (2008), no. 1, 419--443.

23. Amir Beck, Marc Teboulle and Zahar Chikishev, Iterative Minimization Schemes for Solving the Single Source Localization Problem, SIAM Journal on Optimization 19 (2008), no. 3, 1397--1416.

24. Amir Beck and Marc Teboulle, A Convex Optimization Approach for Minimizing the Ratio of Indefinite Quadratic Functions over an Ellipsoid, Mathematical Programming, 118 (2009), no.1 13-35. 

25. Amir Beck, Convexity Properties Associated with Nonconvex Quadratic Matrix Functions and Applications to Quadratic Programming Journal of Optimization Theory and Applications 142 (2009), no.1, 1-29.

26. Amir Beck and Marc Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, 2 (2009), no. 1, 183--202  MATLAB files.

27. Amir Beck and Aharon Ben-Tal, Duality in Robust Optimization: Primal Worst Equals Dual Best, Operations Research Letters 37(2009), issue 1, 1--9. 

28. Amir Beck and Marc Teboulle, Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems IEEE Trans. Image Proc. vol. 18, no. 11, November 2009, 2419--2434. MATLAB files

29. Amir Beck, Aharon Ben-Tal and Luba Tetruashvili, A Sequential Parametric Convex Approximation Method with Applications to Nonconvex Truss Topology Design Problems, Journal of Global Optimization, 47 (2010) no.1, 29--51.

30. Amir Beck and Marc Teboulle, On Minimizing Quadratically Constrained Ratio of Two Quadratic Functions, Journal of Convex Analysis 17(2010), No. 3&4, 789--804.

31. Amir Beck, Aharon Ben-Tal, Nili Guttmann-Beck, Luba Tetruashvili, The CoMirror algorithm for solving nonsmooth constrained convex problems, Operations Research Letters, volume 38, issue 6 (2010), 493–398.

32. Amir Beck and Yonina C. Eldar, Structured Total Maximum Likelihood: An Alternative to Structured Total Least-Squares, SIAM J. Matrix. Anal. Appl. vol. 31, no. 5 (2010) 2623--2649. MATLAB files.

33. Amir Beck and Dror Pan, "On the Solution of the GPS Localization and Circle Fitting Problems", SIAM J. Optim. Vol. 22, No. 1, 108--134 (2011)

34. Amir Beck, Aharon Ben-Tal and Luba Tetruashvili, "A Sequential Ascending Parameter Method for Solving Constrained Minimization Problems", SIAM J. Optim. vol 12 (2012), No. 1, 244-260.

35. Amir Beck, Yoel Drori and Marc Teboulle, "A new SDP relaxation scheme for a class of quadratic matrix problems", Operations Research Letters, vol. 40 (2012), no. 4, 298--302.

36. Amir Beck and Marc Teboulle, "Smoothing and First Order Methods: A Unified Framework", SIAM J. Optim. vol. 22 (2012), No. 2, 557--580.

37. Amir Beck and Shoham Sabach, "An Improved Ellipsoid Method for Solving Convex Differentiable Optimization Problems",Operations Research Letters 40 (2013), 541—545.

38. Amir Beck and Yonina C. Eldar, "Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms" SIAM J. Optim. , vol. 23(2013), no. 3, 1480–1509. MATLAB files

39. Amir Beck and Luba Tetruashvili, "On the Convergence of Block Coordinate Descent Type Methods", SIAM J. Optim, vol. 23(2013), no. 2, 2037–2060, 2013.

40. Amir Beck and Shoham Sabach, "A First Order Method for Finding Minimal Norm-Like Solutions of Convex Optimization Problems", Mathematical Programming, 147 (2014), 25-46.

41. A. Beck, "The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems", J. Optim. Theory and Appl. (2014) 162: 892--919.

42. Yoav Shechtman, Amir Beck and Yonina C. Eldar, "GESPAR: Efficient Phase Retrieval of Sparse Signals", IEEE Trans. Signal Proc., (2014) vol 62, no. 4, 928--938.

43. Amir Beck and Marc Teboulle, ""A Fast Dual Proximal Gradient Algorithm for Convex Minimization and Applications" Operations Research Letters 42(2014) 1-6

44. A. Beck, Angelia Nedic, Asuman Ozdaglar and Marc Teboulle, "An O(1/k) Gradient Method for Network Resource Allocation Problem", IEEE Trans. on Control and Network Systems, (2014), vol. 1, no. 1.

45. Zhao Tan, Yonina C. Eldar, Amir Beck and Arye Nehorai, "Smoothing and Decomposition for Analysis Sparse Recovery", IEEE. Trans. Signal Proc. (2014), vol. 62, no. 7, 1762--1774.

46. Amir Beck and Shoham Sabach, "Weiszfeld’s Method: Old and New Results", J. Optim. Theory and Appl. (2015) vol. 164, no. 1, 1--40. 

47. Amir Beck, "On the Convergence of Alternating Minimization for Convex Programming with Applications to Iteratively Reweighted Least Squares and Decomposition Schemes", SIAM J. Optim. vol. 25, no. 1 (2015), 185--209.

48. Amir Beck, Edouard Pauwels and Shoham Sabach, "The Cyclic Block Conditional Gradient Method for Convex Optimization Problems", SIAM J. Optim., vol. 25(2015), no. 4, 2024—2049.

49. Amir Beck, Luba Tetruashvili, Yakov Vaisbourd and Ariel Shemtov, "Rate of Convergence Analysis of Dual-Based Variables Decomposition Methods for Strongly Convex Problems", Operations Research Letters, vol. 44, no. 1 (2016), 61--66.

50. Amir Beck and Nadav Hallak, "On the Minimization Over Sparse Symmetric Sets: Projections, Optimality Conditions and Algorithms", Mathematics of Operations Research, vol. 41, no. 1 (2016), 196--223.

51. Amir Beck and Yakov Vaisbourd, "The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms", J. Optim. Theory and Appl., vol. 170, no. 1 (2016), 119--143 MATLAB files

52. Amir Beck, Shoham Sabach and Marc Teboulle, "An Alternating Semiproximal Method for Nonconvex Regularized Structured Total Least Squares Problems", SIAM J. Matrix Anal. Appl., vol. 37, no. 3 (2016), 1129--1150.

53. Amir Beck and Shimrit Shtern, "Linearly Convergent Away-Step Conditional Gradient for Non-Strongly Convex Functions", Mathematical Programming, vol. 164 (2017), issue 1-2, 1--27. 

54. Amir Beck, Edouard Pauwels and Shoham Sabach, "Primal and Dual Predicted Decrease Approximation Methods",  Mathematical Programming, vol. 167 (2018), issue 1, 37--73.

55. Amir Beck and Dror Pan, "A Branch and Bound Algorithm for Nonconvex Quadratic Optimization with Ball and Linear Constraints", Journal of Global Optimization, vol. 69, no. 2 (2017), 309--342. MATLAB files

56. Edouard Pauwels, Amir Beck, Yonina Eldar and Shoham Sabach, "On Fienup Methods for Sparse Phase Retrieval",  IEEE Transactions on Signal Processing, vol. 66, no. 4, Feb. 2018.

57. Amir Beck and Nadav Hallak, "Proximal Mapping for Symmetric Penalty and Sparsity", SIAM J. Optim., vol. 28, no. 1 (2018), 496--527.

58. Amir Beck, Yuval Beck, Yoash Levron, Alex Shtof, Luba Tetruashvili, "Globally Solving a Class of Optimal Power Flow Problems in Radial Networks by Tree Reduction", Journal of Global Optimization, vol. 72, no. 3 (2018), 373--402.  Software's website

59. Amir Beck and Nadav Hallak, "Optimization Problems Involving Group Sparsity Terms",  Mathematical Programming, vol. 178 (2019), 39--67.

60. Amir Beck and Yakov Vaisbourd, "Globally Solving the Trust Region Subproblem Using Simple First-Order Methods", SIAM J. Optim., vol. 28, no. 3 (2018), 1951--1967.

61. Amir Beck and Nili Guttmann-Beck, "FOM - A MATLAB Toolbox of First Order Methods for Solving Convex Optimization Problems",  Optimization Methods and Software, vol. 34, no. 1 (2019), 172--193. Software's website

62. Jeremias Sulam, Aviad Aberdam, Amir Beck, Michael Elad, "On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 42, no. 8 (2020), 1968--1980.

63. Amir Beck and Nadav Hallak, "On the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions Methods", SIAM J. Optim. vol. 30 (2020), no. 1, 56—79.

64. Amir Beck and Marc Teboulle, "Dual Randomized Coordinate Descent Method for Solving a Class of Nonconvex Problems", SIAM J. Optim., vol. 31, no. 3 (2021), 1877--1896.

65. Aviad Aberdam and Amir Beck, "An Accelerated Coordinate Gradient Descent Algorithm  for Non-Separable Composite Optimization", J. Optim. Theory, 193 (2022), 219--246.

66. Amir Beck and Yehonathan Refael, "Sparse Regularization via Bidualization", Journal of Global Optimization, 82, (2022), 463--482.

67. Amir Beck and Raz Sharon, "New Results on Multi-Dimensional Linear Discriminant Analysis", Oper. Res. Lett. 50 (2022), no. 1, 1--7. 

68. Amir Beck and Nadav Hallak, ``The Regularized Feasible Directions Method for Nonconvex Optimization", Oper. Res. Lett. 50 (2022), no. 5, 517--523.

69. Amir Beck and Israel Rosset, "A Dynamic Smoothing Technique for a Class of Nonsmooth Optimization Problems of Manifolds",  SIAM J. Optim, 33 (2023), no.3, 1473--1493.

70. Amir Beck and Raz Sharon, "A Branch and Bound Method for Solving the Max-Min Linear Discriminant Analysis Problem", Optimization Methods and Software, 38 (2023), no. 5, 1031--1057.

Book Chapters

1. Amir Beck and Marc Teboulle, Gradient-Based Algorithms with Applications to Signal Recovery Problems, in "Convex Optimization in Signal Processing and Communications". Editors: Yonina Eldar and Daniel Palomar. Cambridge University Press, 2009. 

2. Amir Beck and Marc Teboulle, A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems. In the book "Fixed-Point Algorithms for Inverse Problems in Science and Engineering", part of the Springer Verlag series Optimization and Its Applications, 2011.

3. Amir Beck and Dror Pan, Convergence of an Inexact Majorization-Minimization Method for Solving a Class of Composite Optimization Problems in the book "Large Scale and Distributed Optimization". Editors: Pontus Gisellson and Andrea Rantzer, part of Springer's Lectures notes in Mathematics 2018. 

Ph.D Thesis

Amir Beck under the supervision of Marc Teboulle (2003), "Convergence Rate Analysis of Gradient Based Algorithms"