{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/convex-optimization-algorithms-and-complexity","title":"Convex Optimization: Algorithms and Complexity","arxiv_id":"1405.4980","date":"2014-05-20","proceeding":null,"authors":["Sébastien Bubeck"],"abstract":"This monograph presents the main complexity theorems in convex optimization\nand their corresponding algorithms. Starting from the fundamental theory of\nblack-box optimization, the material progresses towards recent advances in\nstructural optimization and stochastic optimization. Our presentation of\nblack-box optimization, strongly influenced by Nesterov's seminal book and\nNemirovski's lecture notes, includes the analysis of cutting plane methods, as\nwell as (accelerated) gradient descent schemes. We also pay special attention\nto non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror\ndescent, and dual averaging) and discuss their relevance in machine learning.\nWe provide a gentle introduction to structural optimization with FISTA (to\noptimize a sum of a smooth and a simple non-smooth term), saddle-point mirror\nprox (Nemirovski's alternative to Nesterov's smoothing), and a concise\ndescription of interior point methods. In stochastic optimization we discuss\nstochastic gradient descent, mini-batches, random coordinate descent, and\nsublinear algorithms. We also briefly touch upon convex relaxation of\ncombinatorial problems and the use of randomness to round solutions, as well as\nrandom walks based methods.","url_abs":"http://arxiv.org/abs/1405.4980v2","url_pdf":"http://arxiv.org/pdf/1405.4980v2.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":"convex-optimization-algorithms-and-complexity","repo_url":"https://github.com/Coolgiserz/NLP_starter","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"convex-optimization-algorithms-and-complexity","repo_url":"https://github.com/stephenbeckr/AIMS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"convex-optimization-algorithms-and-complexity","repo_url":"https://github.com/stephenbeckr/CambridgeOptimisationCourse","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1405.4980","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}