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A filter-trust-region method for unconstrained optimization. (English) Zbl 1122.90074
Summary: A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by {\it R. Flechter} and {\it S. Leyffer} [Math. Program. 91, No. 2 (A), 239--269 (2002; Zbl 1049.90088)], it extends an existing technique of {\it N. I. M. Gould, S. Leyffer} and {\it P. Toint} [SIAM J. Optim. 15, No. 1, 17-38 (2004; Zbl 1075.65075)] for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algorithm is shown to be globally convergent to at least one second-order critical point, and numerical experiments indicate that it is very competitive with more classical trust-region algorithms.

90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
90C26Nonconvex programming, global optimization
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