带稀疏约束的分裂可行问题的算法
The Solution of Sparsity-Constrained Split Feasibility Problem

作者: 畅含笑 , 孙军 , 屈彪 :曲阜师范大学管理学院,山东 日照;

关键词: 分裂可行问题稀疏约束IHT算法稳定点Split Feasible Problem Sparsity-Constrained IHT Algorithm Stationery

摘要: 本文,我们主要研究带稀疏约束的分裂可行问题。在某些合理的假设下用IHT算法,得到了带稀疏约束的分裂可行问题的稳定点及给出在局部收敛性分析中起到了重要作用的结论。

Abstract: In this paper, we mainly study the solution of sparsity-constrained split feasibility problem. Under some reasonable assumptions, we use IHT algorithm to get the stationary points of sparsity-  constrained split feasibility problem and get a conclusion which plays an important role in local convergence analysis.

文章引用: 畅含笑 , 孙军 , 屈彪 (2016) 带稀疏约束的分裂可行问题的算法。 应用数学进展, 5, 269-275. doi: 10.12677/AAM.2016.52034

参考文献

[1] Bardsley, J. and Nagy, J. (2006) Covariance-Preconditioned Iterative Methods for Nonnegativity Constrainted Astro-nomical. SIAM Journal, 27, 1184-1198.

[2] Bruckstein, A.M., Donoho, D.L. and Elad, M. (2009) From Sparse Solu-tions of Systems of Equations to Sparse Modeling of Signals and Images. SIAM Review, 51, 34-81.
http://dx.doi.org/10.1137/060657704

[3] Bruckstein, A.M., Elad, M. and Zibulevsky, M. (2008) On the Uni-queness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations. IEEE Transactions on Information Theory, 54, 4813-4820.
http://dx.doi.org/10.1109/TIT.2008.929920

[4] Donoho, D.L. and Tanner, J. (2005) Sparse Nonnegative Solu-tions of Underdetermined Linear Equations by Linear Programming. Proceedings of the National Academy of Sciences of the United States of America, 102, 9446-9951.
http://dx.doi.org/10.1073/pnas.0502269102

[5] Beck, A. and Eldar, Y. (2013) Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms. SIAM Journal, 23, 1480-1509.
http://dx.doi.org/10.1137/120869778

[6] Bahmani, S., Raj, B. and Boufounos, P.T. (2013) Greedy Sparsi-ty-Constraind Optimization. Journal of Machine Learning Research, 14, 807-841.

[7] Cartis, C. and Thompson, A. (2013) A New and Improved Quantitative Recovery Analysis for Iterative Hard Thresholding Algorithms in Compressed Sensing. arXiv:1309.5406.pdf.

[8] Tropp, J. (2004) Greed Is Good: Algorithmic Results for Sparse Approximation. IEEE Transactions on Information Theory, 50, 2231-2242.
http://dx.doi.org/10.1109/TIT.2004.834793

[9] Censor, Y. and Elfving, T. (1994) A Multiprojection Algorithm Using Bregman Projection in a Product Space. Numerical Algorithms, 8, 221-239.
http://dx.doi.org/10.1007/BF02142692

[10] Bertsekas, D.P. (1999) Nonlinear Programming. 2nd Edition, Athena Scientific, Belmont.

[11] Wang, C., Liu, Q. and Ma, C. (2013) Smoothing SQP Algorithm for Semismooth Equations with Box Constraints. Computational Optimization and Applications, 55, 399-425.
http://dx.doi.org/10.1007/s10589-012-9524-5

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