Stopping rules and backward error analysis for bound-constrained optimization

Serge Gratton, Mélodie Mouffe, Philippe Toint

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Termination criteria for the iterative solution of bound-constrained optimization problems are examined in the light of backward error analysis. It is shown that the problem of determining a suitable perturbation on the problem's data corresponding to the definition of the backward error is analytically solvable under mild assumptions. Moreover, a link between existing termination criteria and this solution is clarified, indicating that some standard measures of criticality may be interpreted in the sense of backward error analysis. The backward error problem is finally considered from the multicriteria optimization point of view and some numerical illustration is provided. © 2011 Springer-Verlag.
Original languageEnglish
Pages (from-to)163-187
Number of pages25
JournalNumerische Mathematik
Issue number1
Publication statusPublished - 1 Sep 2011



  • stopping criterion
  • bound constraints
  • backward error
  • multicriteria optimization.
  • Nonlinear optimization

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