{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T17:53:56Z","timestamp":1780077236235,"version":"3.54.0"},"reference-count":283,"publisher":"Emerald","issue":"1-2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,12,15]]},"abstract":"<jats:p>This monograph covers some recent advances in a range of acceleration techniques frequently used in convex optimization. We first use quadratic optimization problems to introduce two key families of methods, namely momentum and nested optimization schemes. They coincide in the quadratic case to form the Chebyshev method.<\/jats:p>\n                  <jats:p>We discuss momentum methods in detail, starting with the seminal work of Nesterov [1] and structure convergence proofs using a few master templates, such as that for optimized gradient methods, which provide the key benefit of showing how momentum methods optimize convergence guarantees. We further cover proximal acceleration, at the heart of the Catalyst and Accelerated Hybrid Proximal Extragradient frameworks, using similar algorithmic patterns.<\/jats:p>\n                  <jats:p>Common acceleration techniques rely directly on the knowledge of some of the regularity parameters in the problem at hand. We conclude by discussing restart schemes, a set of simple techniques for reaching nearly optimal convergence rates while adapting to unobserved regularity parameters.<\/jats:p>","DOI":"10.1561\/2400000036","type":"journal-article","created":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T08:34:15Z","timestamp":1639557255000},"page":"1-245","source":"Crossref","is-referenced-by-count":43,"title":["Acceleration Methods"],"prefix":"10.1108","volume":"5","author":[{"given":"Alexandre","family":"d\u2019Aspremont","sequence":"first","affiliation":[{"name":"CNRS & Ecole Normale Sup\u00e9rieure , ,","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Damien","family":"Scieur","sequence":"additional","affiliation":[{"name":"Samsung SAIT AI Lab & Mila , ,","place":["Montreal, Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrien","family":"Taylor","sequence":"additional","affiliation":[{"name":"INRIA & Ecole Normale Sup\u00e9rieure , ,","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","published-online":{"date-parts":[[2021,12,15]]},"reference":[{"issue":"2","key":"2026033014423757600_ref001","first-page":"372","article-title":"A method of solving a convex programming problem with convergence rate O(1\/k2)","volume":"27","author":"Nesterov","year":"1983","journal-title":"Soviet Mathematics Doklady"},{"issue":"1","key":"2026033014423757600_ref002","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"1","key":"2026033014423757600_ref003","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s10107-013-0653-0","article-title":"Performance of first-order methods for smooth convex minimization: A novel approach","volume":"145","author":"Drori","year":"2014","journal-title":"Mathematical Programming"},{"issue":"1","key":"2026033014423757600_ref004","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s10107-015-0949-3","article-title":"Optimized first-order methods for smooth convex minimization","volume":"159","author":"Kim","year":"2016","journal-title":"Mathematical Programming"},{"key":"2026033014423757600_ref005","volume-title":"Introductory Lectures on Convex Optimization","author":"Nesterov","year":"2003"},{"key":"2026033014423757600_ref006","unstructured":"P.\n              Tseng\n            \n          , On accelerated proximal gradient methods for convex-concave optimization, 2008. 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