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This not only\u00a0provides an elegant and flexible framework to parametrize and reinterpret existing stepsize schemes, but\u00a0it also gives inspiration for new flexible and tunable families of steplengths. In particular, we analyze and extend the adaptive Barzilai\u2013Borwein method to a new family of stepsizes. While this family exploits negative values for the target, we also consider positive targets. We present a convergence analysis for quadratic problems extending results by Dai and Liao (IMA J Numer Anal 22(1):1\u201310, 2002), and carry out experiments outlining the potential of the approaches.<\/jats:p>","DOI":"10.1007\/s10589-023-00455-6","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T17:46:50Z","timestamp":1676483210000},"page":"75-106","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A harmonic framework for stepsize selection in gradient methods"],"prefix":"10.1007","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5672-3094","authenticated-orcid":false,"given":"Giulia","family":"Ferrandi","sequence":"first","affiliation":[]},{"given":"Michiel E.","family":"Hochstenbach","sequence":"additional","affiliation":[]},{"given":"Nata\u0161a","family":"Kreji\u0107","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,15]]},"reference":[{"issue":"1","key":"455_CR1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. 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