{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T03:12:35Z","timestamp":1772939555360,"version":"3.50.1"},"reference-count":53,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:p>We present and analyze an away-step Frank\u2013Wolfe method for the convex optimization problem [Formula: see text], where f is a \u03b8-logarithmically homogeneous self-concordant barrier, [Formula: see text] is a linear operator that may be noninvertible, [Formula: see text] is a linear function, and [Formula: see text] is a nonempty polytope. The applications of primary interest include D-optimal design, inference of multivariate Hawkes processes, and total variation-regularized Poisson image deblurring. We establish affine-invariant and norm-independent global linear convergence rates of our method in terms of both the objective gap and the Frank\u2013Wolfe gap. When specialized to the D-optimal design problem, our results settle a question left open since Ahipasaoglu et al. [Ahipasaoglu SD, Sun P, Todd MJ (2008) Linear convergence of a modified Frank\u2013Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optim. Methods Software 23(1):5\u201319]. We also show that the iterates generated by our method will land on and remain in a face of [Formula: see text] within a bounded number of iterations, which can lead to improved local linear convergence rates (for both the objective gap and the Frank\u2013Wolfe gap). We conduct numerical experiments on D-optimal design and inference of multivariate Hawkes processes, and our results not only demonstrate the efficiency and effectiveness of our method compared with other principled first-order methods but also, corroborate our theoretical results quite well.<\/jats:p>\n                  <jats:p>Funding: This work was supported by the Air Force Office of Scientific Research [Grant FA9550-22-1-0356].<\/jats:p>","DOI":"10.1287\/moor.2023.0281","type":"journal-article","created":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T08:30:21Z","timestamp":1737361821000},"page":"35-59","source":"Crossref","is-referenced-by-count":1,"title":["New Analysis of an Away-Step Frank\u2013Wolfe Method for Minimizing Log-Homogeneous Barriers"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8226-9243","authenticated-orcid":false,"given":"Renbo","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Business Analytics, Tippie College of Business, University of Iowa, Iowa City, Iowa 52242"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1080\/10556780701589669"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1972.1054753"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342371"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2016.0817"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-1069-4"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1137\/0306032"},{"key":"B7","unstructured":"Carderera A, Besan\u00e7on M, Pokutta S (2021) Simple steps are all you need: Frank\u2013Wolfe and generalized self-concordant functions.\n                      35th Conf. 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