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College Colloquium--On Convergence of Iterative Thresholding Algorithms to Global Solution for Nonconvex Sparse Optimization

发布日期:2024-11-23点击数:

报告人:胡耀华 教授(深圳大学)

时间:2024年11月24日 15:00-

地点:极速赛车官网 LD416


摘要:This talk aims to find an approximate global solution or true sparse solution of an under-determined linear system. For this purpose, we propose two types of iterative thresholding algorithms with the continuation technique and the truncation technique respectively. We introduce a notion of limited shrinkage thresholding operator and apply it, together with the restricted isometry property, to show that the proposed algorithms converge to an approximate global solution or true sparse solution within a tolerance relevant to the noise level and the limited shrinkage magnitude. Applying the obtained results to nonconvex regularization problems with SCAD, MCP and Lp penalty and utilizing the recovery bound theory, we establish the convergence of their proximal gradient algorithms to an approximate global solution of nonconvex regularization problems.

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