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

C. P. Brás, José Mário Martínez, M. Raydan

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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.

Original languageEnglish
JournalComputational Optimization And Applications
Volume75
Issue number1
Early online date1 Oct 2019
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Cubic modeling
  • Disk packing problem
  • Lanczos method
  • Newton-type methods
  • Smooth unconstrained minimization
  • Subspace minimization
  • Trust-region strategies

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