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Instead of computing the exact Levenberg\u2013Marquardt direction, we introduce an inexact direction which simplifies the calculations and reduces the computational cost. Global convergence results are established for the proposed method endowed with a non-monotone line search. A series of numerical experiments on different classes of the problem are carried out and indicate that the new Projected Inexact Levenberg\u2013Marquardt algorithm is competitive with well-established alternatives such as algorithms based on proximal gradient or alternating minimization methods.<\/jats:p>","DOI":"10.1007\/s10957-026-02950-2","type":"journal-article","created":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T05:53:05Z","timestamp":1773467585000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Projected Inexact Levenberg-Marquardt Method for the Completely Positive Matrix Factorization"],"prefix":"10.1007","volume":"209","author":[{"given":"Roger","family":"Behling","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8673-1319","authenticated-orcid":false,"given":"Douglas","family":"Gon\u00e7alves","sequence":"additional","affiliation":[]},{"given":"Hugo","family":"Lara","sequence":"additional","affiliation":[]},{"given":"Harry","family":"Oviedo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,14]]},"reference":[{"issue":"1","key":"2950_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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