@article {13843,
	title = {Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization},
	journal = {Computational Optimization and Applications},
	volume = {75},
	year = {2020},
	pages = {169-205},
	abstract = {<p>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.</p>
},
	url = {https://link.springer.com/article/10.1007/s10589-019-00138-1},
	author = {C. P. Br{\'a}s and J. M. Martinez and M. Raydan}
}
