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The method is designed to minimize the sum of a twice continuously differentiable function <jats:italic>f<\/jats:italic> and a convex (possibly non-smooth and extended-valued) function <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varphi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c6<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Instead of controlling a step size by a line search procedure, we update the regularization parameter in a suitable way, based on the success of the previous iteration. The global convergence of the sequence of iterations and its superlinear convergence rate under a local H\u00f6lderian error bound assumption are shown. Notably, these convergence results are obtained without requiring a global Lipschitz property for <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \\nabla f $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u2207<\/mml:mi>\n                    <mml:mi>f<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which, to the best of the authors\u2019 knowledge, is a novel contribution for proximal Newton methods. To highlight the efficiency of our approach, we provide numerical comparisons with an IRPNM using a line search globalization and a modern FISTA-type method.<\/jats:p>","DOI":"10.1007\/s10589-024-00600-9","type":"journal-article","created":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T18:01:57Z","timestamp":1723831317000},"page":"585-624","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An inexact regularized proximal Newton method without line search"],"prefix":"10.1007","volume":"89","author":[{"given":"Simeon","family":"vom Dahl","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2897-2509","authenticated-orcid":false,"given":"Christian","family":"Kanzow","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,16]]},"reference":[{"issue":"1","key":"600_CR1","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. 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