Global convergence of a non-monotone trust-region filter algorithm for nonlinear programming.

*(English)* Zbl 1130.90399
Hager, William W. (ed.) et al., Multiscale optimization methods and applications. Selected papers based on the presentation at the conference, Gainesville, FL, USA, February 26–28, 2004. New York, NY: Springer (ISBN 0-387-29549-6/hbk). Nonconvex Optimization and Its Applications 82, 125-150 (2006).

A non-monotone variant of the trust-region SQP-filter algorithm analyzed in

*D. F. Fletcher, B. Guo* and

*T.A.G. Langrish* [Appl. Math. Modelling 25, No. 8, 635–653 (2001;

Zbl 1076.76535)] 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.

##### MSC:

90C30 | Nonlinear programming |

90C55 | Methods of successive quadratic programming type |