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Nonlinear programming without a penalty function or a filter

Nick Gould (nick.gould***at***comlab.ox.ac.uk)
Philippe Toint (philippe.toint***at***fundp.ac.be)

Abstract: A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or 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.

Keywords: Nonlinear optimization, equality constraints, numerical algorithms, global convergence.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 3: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: Mathematical Programming A, DOI 10.1007/s10107-008-0244-7

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Entry Submitted: 04/18/2007
Entry Accepted: 04/18/2007
Entry Last Modified: 02/20/2009

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