In this paper, we propose and analyze adaptive projected gradient thresholding(APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergenc...In this paper, we propose and analyze adaptive projected gradient thresholding(APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergence will be demonstrated, and in addition, the bound of the number of iterations is established in some special cases. Under suitable assumptions, it is proved that any accumulation point of the sequence generated by the APGT methods is a local minimizer of the underdetermined linear system. Moreover, the APGT methods, under certain conditions, can find all s-sparse solutions for accurate measurement cases and guarantee the stability and robustness for flawed measurement cases. Numerical examples are presented to show the accordance with theoretical results in compressed sensing and verify high out-of-sample performance in index tracking.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11101325,11271297,71371152 and 71171158)partially supported by the Foundations of the Key Discipline of the State Ethnic Affairs Commission
文摘In this paper, we propose and analyze adaptive projected gradient thresholding(APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergence will be demonstrated, and in addition, the bound of the number of iterations is established in some special cases. Under suitable assumptions, it is proved that any accumulation point of the sequence generated by the APGT methods is a local minimizer of the underdetermined linear system. Moreover, the APGT methods, under certain conditions, can find all s-sparse solutions for accurate measurement cases and guarantee the stability and robustness for flawed measurement cases. Numerical examples are presented to show the accordance with theoretical results in compressed sensing and verify high out-of-sample performance in index tracking.
