Nonlinear programming without a penalty function or a filter

Nick Gould, Philippe Toint

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A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate that the method performs well. © 2008 Springer-Verlag.
Original languageEnglish
Pages (from-to)155-196
Number of pages42
JournalMathematical Programming
Issue number1
Publication statusPublished - 1 Mar 2010


  • global convergence
  • equality constraints
  • numerical algorithms
  • Nonlinear optimization


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