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Imaging Sci., 2 (2009), pp. 183--202] that is widely used for minimizing composite convex functions with a nonsmooth term such as the $\\ell_1$ regularizer. In particular, this paper shows that FISTA corresponds to an optimized approach to accelerating the proximal gradient method with respect to a worst-case bound of the cost function. This paper then proposes a new algorithm that is derived by instead optimizing the step coefficients of the proximal gradient method with respect to a worst-case bound of the composite gradient mapping. The proof is based on the worst-case analysis called the performance estimation problem in [Y. Drori and M. Teboulle, Math. Program., 145 (2014), pp. 451--482].<\/jats:p>","DOI":"10.1137\/16m108940x","type":"journal-article","created":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T12:03:05Z","timestamp":1517313785000},"page":"223-250","source":"Crossref","is-referenced-by-count":63,"title":["Another Look at the Fast Iterative Shrinkage\/Thresholding Algorithm (FISTA)"],"prefix":"10.1137","volume":"28","author":[{"given":"Donghwan","family":"Kim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeffrey A.","family":"Fessler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TCNS.2014.2309751"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2028250"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2013.10.007"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-015-0746-4"},{"key":"atypb6","first-page":"185","author":"Combettes P. 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