Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization

C. P. Brás (), J. M. Martínez () and M. Raydan ()
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C. P. Brás: UNL
J. M. Martínez: University of Campinas
M. Raydan: UNL

Computational Optimization and Applications, 2020, vol. 75, issue 1, No 7, 169-205

Abstract: Abstract 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.

Keywords: Smooth unconstrained minimization; Cubic modeling; Subspace minimization; Trust-region strategies; Newton-type methods; Lanczos method; Disk packing problem (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-019-00138-1

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