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Recent theoretical investigations have\ndemonstrated their superiority over the convex counterparts in several sparse\nlearning settings. However, solving the non-convex optimization problems\nassociated with non-convex penalties remains a big challenge. A commonly used\napproach is the Multi-Stage (MS) convex relaxation (or DC programming), which\nrelaxes the original non-convex problem to a sequence of convex problems. This\napproach is usually not very practical for large-scale problems because its\ncomputational cost is a multiple of solving a single convex problem. In this\npaper, we propose a General Iterative Shrinkage and Thresholding (GIST)\nalgorithm to solve the nonconvex optimization problem for a large class of\nnon-convex penalties. The GIST algorithm iteratively solves a proximal operator\nproblem, which in turn has a closed-form solution for many commonly used\npenalties. At each outer iteration of the algorithm, we use a line search\ninitialized by the Barzilai-Borwein (BB) rule that allows finding an\nappropriate step size quickly. The paper also presents a detailed convergence\nanalysis of the GIST algorithm. The efficiency of the proposed algorithm is\ndemonstrated by extensive experiments on large-scale data sets.","url_abs":"http://arxiv.org/abs/1303.4434v1","url_pdf":"http://arxiv.org/pdf/1303.4434v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-general-iterative-shrinkage-and","repo_url":"https://github.com/EvanZhuang/MRI-Reconstruction-with-Sparse-Optimization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"a-general-iterative-shrinkage-and","repo_url":"https://github.com/KeSyren/paper-GC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"a-general-iterative-shrinkage-and","repo_url":"https://github.com/iancovert/Neural-GC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"a-general-iterative-shrinkage-and","repo_url":"https://github.com/icc2115/Neural-GC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"sparse-learning","task_name":"Sparse Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1303.4434","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1303.4434"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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