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The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.<\/jats:p>","DOI":"10.1007\/s10589-021-00342-y","type":"journal-article","created":{"date-parts":[[2022,1,6]],"date-time":"2022-01-06T06:02:25Z","timestamp":1641448945000},"page":"369-395","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On a primal-dual Newton proximal method for convex quadratic programs"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3545-6898","authenticated-orcid":false,"given":"Alberto","family":"De Marchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,6]]},"reference":[{"key":"342_CR1","unstructured":"Ali, A., Wong, E., Kolter, J.Z.: A semismooth Newton method for fast, generic convex programming. 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