Brás, C. P.Martínez, José MárioRaydan, M.2020-05-142022-03-092020-01-010926-6003PURE: 15494912PURE UUID: 3479327b-691a-4fa6-833f-43f539ba05bcScopus: 85074596050WOS: 000490886300001http://hdl.handle.net/10362/97712PRONEX-CNPq/FAPERJ (E-26/111.449/2010-APQ1), CEPID-Industrial Mathematics/FAPESP (Grant 2011/51305-02), FAPESP (Projects 2013/05475-7 and 2013/07375-0). Fundacao para a Ciencia e a Tecnologia- project UID/MAT/00297/2019 (CMA).We present a new algorithm for solving large-scale unconstrained optimization problems that uses cubic models, matrix-free subspace minimization, and secant-type parameters for defining the cubic terms. We also propose and analyze a specialized trust-region strategy to minimize the cubic model on a properly chosen low-dimensional subspace, which is built at each iteration using the Lanczos process. For the convergence analysis we present, as a general framework, a model trust-region subspace algorithm with variable metric and we establish asymptotic as well as complexity convergence results. Preliminary numerical results, on some test functions and also on the well-known disk packing problem, are presented to illustrate the performance of the proposed scheme when solving large-scale problems.596238engCubic modelingDisk packing problemLanczos methodNewton-type methodsSmooth unconstrained minimizationSubspace minimizationTrust-region strategiesControl and OptimizationComputational MathematicsApplied Mathematicsjournal article10.1007/s10589-019-00138-1https://www.scopus.com/pages/publications/85074596050