<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. P. Brás</style></author><author><style face="normal" font="default" size="100%">J. M. Martinez</style></author><author><style face="normal" font="default" size="100%">M. Raydan</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization</style></title><secondary-title><style face="normal" font="default" size="100%">Computational Optimization and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s10589-019-00138-1</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">75</style></volume><pages><style face="normal" font="default" size="100%">169-205</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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