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Associate Professor Amir Beck

 
 
General Information


Prof. Beck received the B.Sc. degree in pure mathematics Cum Laude in 1991, the M.sc. degree in operations research Suma Cum laude and the Ph.D. degree in operations research -- all from Tel Aviv University (TAU), Tel Aviv, Israel. From 2003 to  2005 he was a Postdoctoral Fellow at the Minerva Optimization Center, Technion, Haifa, Israel. Prof. Beck joined the Faculty of Industrial Engineering and Management in 2005.

 
 
Current Research Projects
  • Nonconvex quadratic optimization: theory, algorithms and applications.

  • Development and analysis of first order methods for large-scale optimization problems.

  • Optimization techniques in numerical linear algebra.

  • Conic programming and applications to signal processing and communication.

 
 
Selected Publications

Refereed Papers

  • 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.

  • 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.

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

  • 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.

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

  • 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.

  • 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 http://www.springer.com/.



  • 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.

  • 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.

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

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

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

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


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

  • 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).


  • 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.

  • 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.

  • 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.

  • 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. MATLAB files.

  • 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.

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

  • 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.

  • 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

  • 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.

  • 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.

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

  • 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.

  • 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.

  •  Amir Beck, Aharon Ben-Tal, Nili Guttmann-Beck, Luba Tetruashvili, The CoMirror algorithm for solving nonsmooth constrained convex problems, Operations Research Letters (2010).

  • 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)

  • Amir Beck, Aharon Ben-Tal and Luba Tetruashvili, "A Sequential Ascending Parameter Method for Solving Constrained Minimization Problems", to appear in SIAM J. Optim. (2012)

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    Submitted Papers

  • Amir Beck and Marc Teboulle, "Smoothing and First Order Methods: A Unified Framework".

  • Amir Beck and Luba Tetruashvili, "On The Convergence of Block Coordinate Descent Type Methods".

  • Amir Beck and Shoham Sabach, "A First Order Method for Finding  Minimal Norm-Like Solutions of Convex Optimization Problems".

  • Amir Beck, Yoel Drori and Marc Teboulle, "A new SDP relaxation scheme for a class of quadratic matrix problems".

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    Conference Papers


  • Yonina C. Eldar and Amir Beck, Hidden Convexity Based near Maximum-Likelihood CDMA Detection 39th Annual Conference on Information Sciences and Systems (CISS 2005).

  • Amir Beck, Yonina C. Eldar and Aharon Ben-Tal, MSE Estimation of Multichannel Signals with Model Uncertainties , Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2005), pp. 49-52, Mar. 2005.

  • Yonina C. Eldar and Amir Beck, Hidden Convexity Based near Maximum-Likelihood CDMA Detection 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, A Fast Iterative Shrinkage-Thresholding Algorithm with Application to Wavelet-Based Image Deblurring, Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2009), pp. 693-696, April 2009

    Ph.D Thesis


  • Amir beck Convergence Rate Analysis of Gradient Based Algorithms under the supervision of Marc Teboulle (2003).





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