Randomized Sparse Block Kaczmarz as Randomized Dual Block-Coordinate Descent
References
- [1] H. H. Bauschke and P. L. Combettes. The Baillon-Haddad Theorem Revisited. Journal of Convex Analysis, 17:781-787, 2010.
- [2] A. Beck and L. Tetruashvili. On the Convergence of Block Coordinate Descent Type Methods. SIAM Journal on Optimization, 23(4):2037-2060, 2013.
- [3] D. P. Bertsekas. Nonlinear Programming. Belmont MA: Athena Scientific, 2nd edition, 1999.
- [4] J.-F. Bonnans, J.C. Gilbert, C. Lemaréchal, and C. Sagastizábal. Numerical Optimization - Theoretical and Practical Aspects. Springer Verlag, Berlin, 2006.
- [5] C. Byrne and Y. Censor. Proximity Function Minimization Using Multiple Bregman Projections, with Applications to Split Feasibility and Kullback-Leibler Distance Minimization. Annals of Operations Research, 105(1-4):77-98, 2001.
- [6] J.-F. Cai, S. Osher, and Z. Shen. Convergence of the Linearized Bregman Iteration for l1-norm Minimization. Mathematics of Computation, 78(268):2127-2136, 2009.
- [7] Y. Censor and T. Elfving. A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms, 8(2):221-239, 1994.
- [8] S. Foucart and H. Rauhut. A Mathematical Introduction to Compressive Sensing. Birkhäuser Basel, 2013.
- [9] M. P. Friedlander and P. Tseng. Exact regularization of convex programs. SIAM Journal on Optimization, 18(4):1326-1350, 2007.
- [10] P.C. Hansen and M. Saxild-Hansen. {AIR} tools a {MATLAB} package of algebraic iterative reconstruction methods. Journal of Computational and Applied Mathematics, 236(8):2167 - 2178, 2012. Inverse Problems: Computation and Applications.
- [11] D. A. Lorenz, F. Schöpfer, and S. Wenger. The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations. SIAM Journal on Imaging Science, 7(2):1237-1262, 2014.
- [12] Z. Lu and L. Xiao. On the Complexity Analysis of Randomized Block-Coordinate Descent Methods. CoRR, 2013.
- [13] Z. Q. Luo and P. Tseng. On the convergence of the coordinate descent method for convex differentiable minimization. Journal of Optimization Theory and Applications, 72(1):7-35, January 1992.
- [14] Y. Nesterov. Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems. SIAM Journal on Optimization, 22(2):341-362, 2012.
- [15] S. Petra and C. Schnörr. Average Case Recovery Analysis of Tomographic Compressive Sensing. Linear Algebra and its Applications, 441:168-198, 2014. Special issue on Sparse Approximate Solution of Linear Systems.
- [16] Peter R. and Martin T. Iteration complexity of randomized blockcoordinate descent methods for minimizing a composite function. Mathematical Programming, 144(1-2):1-38, 2014.
- [17] P. Richtárik and M. Takác. Parallel Coordinate Descent Methods for Big Data Optimization. CoRR, abs/1212.0873, 2012.
- [18] P. Richtárik and M. Takác. On Optimal Probabilities in Stochastic Coordinate Descent Methods. CoRR, abs/1310.3438, 2013.
- [19] R.T. Rockafellar and R. J.-B. Wets. Variational Analysis. Springer, 2nd edition, 2009.
- [20] T. Strohmer and R. Vershynin. A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications, 15:262-278, 2009.
- [21] P. Tseng. Convergence and Error Bound for Perturbation of Linear Programs. Computational Optimization and Applications, 13(1-3):221-230, 1999.
- [22] W. Yin, S. Osher, D. Goldfarb, and J. Darbon. Bregman Iterative Algorithms for l1-Minimization with Applications to Compressed Sensing. SIAM Journal on Imaging Sciences, pages 143-168, 2008.
Language: English
Page range: 129 - 149
Submitted on: Jan 1, 2015
Accepted on: Mar 1, 2015
Published on: Apr 22, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
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© 2017 Stefania Petra, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.