Chapter

Multiscale Optimization Methods and Applications

Volume 82 of the series Nonconvex Optimization and Its Applications pp 125-150

Global Convergence of a Non-monotone Trust-Region Filter Algorithm for Nonlinear Programming

  • Nicholas I. M. GouldAffiliated withRutherford Appleton Laboratory, Computational Science and Engineering Department
  • , Philippe L. TointAffiliated withDepartment of Mathematics, University of Namur

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Summary

A non-monotone variant of the trust-region SQP-filter algorithm analyzed in Fletcher et al (SIAM J. Opt. 13(3), 2002, pp. 653–659) is defined, that directly uses the dominated area of the filter as an acceptability criterion for trial points. It is proved that, under reasonable assumptions and for all possible choices of the starting point, the algorithm generates at least a subsequence converging to a first-order critical point.