Prof. Amir Beck

Operations Research and Optimization

Optimization Laboratory



Prof. Amir Beck joined the Faculty of Industrial Engineering and Management at the Technion in 2005. Previously, he completed his M.Sc. and Ph.D. degrees in operations research at Tel Aviv University. From 2003 to 2005 he was a Postdoctoral Fellow at the Minerva Optimization Center.


Amir Beck is a Professor in the Department of Industrial Engineering at The Technion—Israel Institute of Technology. He has published numerous papers, has given invited lectures at international conferences, and was awarded the Salomon Simon Mani Award for Excellence in Teaching and the Henry Taub Research Prize. His research interests are in continuous optimization, including theory, algorithmic analysis, and applications. He is an associate editor of Mathematics of Operations Research, Mathematical Programming Series A, the Journal of Optimization Theory and Applications, Optimization Methods and Software and an area editor for optimization in Operations Research. His research has been supported by various funding agencies, including the Israel Science Foundation, the German-Israeli Foundation, the Binational US-Israel foundation, the Israeli Science and Energy Ministries and the European community.


  • Continuous Optimization: Theory and Algorithms
  • Analysis of First Order Methods in Convex Analysis
  • Decomposition and Block-Descent Type Methods
  • Applications of Convex Optimization Methods in Engineering and Science

Selected Publications

Go to my personal webpage

  1. 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.
  2. 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. 
  3. Amir Beck and Marc Teboulle, Mirror descent and nonlinear projected subgradient methods for convex optimization , Oper. Res. Lett. 31 (2003), no. 3, 167--175. 
  4. 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. 
  5. Amir beck and Marc Teboulle, Global optimality conditions for quadratic optimization problems with binary constraints , SIAM J. Optim. 11 (2000), no. 1, 179--188. 
  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., Ser. B 107, 155-187 (2006). The original publication is avaliable at
  8. Amir Beck, Aharon Ben-Tal and Marc Teboulle Finding a Global Optimal Solution for a Quadratically Constrained Fractiobal Quadratic Problem with Applications to the Regularized Total Least Squares , SIAM J. Matrix Anal. Appl. 28(2):425-445,2006.
  9. 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. 
  10. 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. 
  11. 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.
  12. Amir Beck and Yonina C. Eldar, Doubly Constrained Robust Capon Beamformer with Ellipsoidal Uncertainty Sets, IEEE Trans. Signal Proc. 55 (2), 753-758 (2007). 
  13. Amir Beck and Yonina C. Eldar Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints SIAM J. Optimization, 17 (3), 844-860 (2006). 
  14. Amir Beck, Quadratic Matrix Programming , SIAM J. Optimization 17 (4), 1224-1238 (2006).
  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, Yonina C. Eldar and Aharon Ben-Tal  Mean-Squared Error Estimation of Multichannel Signals, SIAM J. Matrix Anal. Appl. 29 (3), 712-730 (2007). 
  18. 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). 
  19. Amir Beck and Marc Teboulle, A Convex Optimization Approach for Minimizing the Ratio of Indefinite Quadratic Functions over an Ellipsoid, 118 (2009), no.1 13-35. 
  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, 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.
  23. 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 Jounral on Matrix Analysis and Applications 30 (2008), no. 1, 419--443. . 
  24. 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.
  25. Amir Beck and Aharon Ben-Tal, Duality in Robust Optimization: Primal Worst Equals Dual Best, Operations Research Letters 37(2009), issue 1, 1--9. 
  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 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 
  28. 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. 
  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, 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.
  31. 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.
  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, 2623--2649.  MATLAB files.
  33.  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.
  34. 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)
  35. 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.
  36. 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.
  37. Amir Beck and Marc Teboulle, "Smoothing and First Order Methods: A Unified Framework", SIAM J. Optim. vol. 22 (2012), No. 2, 557--580.
  38. 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.
  39. Amir Beck and Shoham Sabach, "A First Order Method for Finding Minimal Norm-Like Solutions of Convex Optimization Problems", to appear in Mathematical Programming
  40. Amir Beck and Marc Teboulle, ""A Fast Dual Proximal Gradient Algorithm for Convex Minimization and Applications" Operations Research Letters 42(2014) 1-6
  41. Amir Beck and Yonina C. Eldar, "Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms" SIAM J. Optim. , vol. 23(2013), no. 3, 1480–1509,.  
  42. Amir Beck and Shoham Sabach, "An Improved Ellipsoid Method for Solving Convex Di fferentiable Optimization Problems",Operations Research Letters 40 (2013), 541—545.
  43. A. Beck, "The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems", J. Optim. Theory and Appl. (2014) 162: 892--919.
  44.  A. Beck, S. Sabach, "Weiszfeld’s Method: Old and New Results",  J. Optim. Theory and Appl. (2015) vol. 164, no. 1, 1--40. 
  45. Y. Shechtman, A. Beck, Y.C. Eldar, "GESPAR: Efficient Phase Retrieval of Sparse Signals", IEEE Trans. Signal Proc., (2014) vol 62, no. 4, 928--938.
  46. Z. Tan, Y.C. Eldar, A. Beck and A. Nehorai, "Smoothing and Decomposition for Analysis Sparse Recovery", IEEE. Trans. Signal Proc. (2014), vol. 62, no. 7, 1762--1774.
  47. A. Beck, A. Nedic, A. Ozdaglar and M. Teboulle, "An O(1/k) Gradient Method for Network Resource Allocation Problem", IEEE Trans. on Control and Network Systems, (2014), vol. 1, no. 1.
  48. A. 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.
  49. A. Beck, L. Tetruashvili, Y. Vaisbourd and A. 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. A. Beck and N. 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. Beck, E. Pauwels and  S. Sabach, "The Cyclic Block Conditional Gradient Method for Convex Optimization Problems",   SIAM J. Optim., vol. 25(2015), no. 4, 2024—2049.
  52. A. Beck and S. Shtern, "Linearly Convergent Away-Step Conditional Gradient for Non-Strongly Convex Functions", accepted for publication in Mathematical Programming.
  53. A. Beck and Y. Vaisbourd, "The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms", J. Optim. Theory and Appl., vol. 170, no. 1 (2016), 119--143 Software Package
  54. A. Beck, S. Sabach and M. 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.
  55. A. Beck, E. Pauwels and S. Sabach, "Primal and Dual Predicted Decrease Approximation Methods", to appear in Mathematical Programming Series B. 

Conference Papers

  • Yonina C. Eldar and Amir Beck,  39th Annual Conference on Information Sciences and Systems (CISS 2005). 
  • Amir Beck, Yonina C. Eldar and Aharon Ben-Tal, , Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2005), pp. 49-52, Mar. 2005. 
  • Yonina C. Eldar and Amir Beck,  IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC-2005). 
  • Y. C. Eldar and A. Beck, "A Chebyshev Center Estimator in Regularized Regression with Bounded Noise," Asilomar Conference on Signals, Systems, and Computers, Oct. 2006. 
  • Y. C. Eldar and A. Beck, "Minimax Regression with Bounded Noise," IEEE-Israel Convention (Electricity 2006). 
  • Amir Beck and Marc Teboulle,, Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2009), pp. 693-696, April 2009 
  • Y. Shechtman, A. Beck and Y.C. Eldar, "Efficient Phase Retrieval of Sparse Signals", 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel.
  • A. Beck and Y.C. Eldar, "Sparse Signal Recovery from Nonlinear Measurements", ICASSP 2013.
  • Y. Shechtman, A. Beck and Y.C. Eldar, "GESPAR: Efficient Sparse Phase Retrieval with Applications to Optics",Proceedings of the 10th International Conference on Sampling Theory and Applications.

Ph.D Thesis

NLO Book








Lecture Slides Based on the Book

  1. Mathematical Preliminaries (without layers/with layers)
  2. Unconstrained Optimization (without layers/with layers)
  3. Least Squares (without layers/with layers)
  4. The Gradient Method (without layers/with layers)
  5. Newton's Method (without layers/with layers)
  6. Convex Sets (without layers/with layers)
  7. Convex Functions (without layers/with layers)
  8. Convex Optimization (without layers/with layers)
  9. Optimization over a Convex Set (without layers/with layers)
  10. Linearly Constrained Problems (without layers/with layers)
  11. The Karush-Kuhn-Tucker Conditions (without layers/with layers)
  12. Duality (without layers/with layers)

FOM book


Optimization Laboratory

Contact Info

Room 521 Bloomfield Building