Approximation accuracy, gradient methods, and error bound for structured convex optimization

• 成果类型: Article; Proceedings Paper
• 署名作者: Tseng, Paul
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0394-2
• 发表日期: 2010
• 页码: 263-295
• 关键词: restricted isometry property; descent method; sparse representations; uncertainty principles; signal recovery; model selection; algorithm; minimization; CONVERGENCE; robust

摘要

Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of interest to bound the solution error relative to the (unknown) solution of the original noiseless problem. Related to this is an error bound for the linear convergence analysis of first-order gradient methods for solving these problems. Example applications include compressed sensing, variable selection in regression, TV-regularized image denoising, and sensor network localization.