Zhihua Zhao, 西安交通大学


Adaptive Projected Gradient Thresholding Methods for Constrained l_0 Problems


In this paper, we propose and analyze Adaptive Projected Gradient Thresholding (APGT) methods for finding sparse solutions of underdetermined linear systems with equality and box constrains. The general convergence will be demonstrated, and in addition we are able to find the bound of the number of iterations 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 systems. Moreover, the APGT methods, under certain conditions, indeed 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.


Fengmin Xu

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