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A nonmonotone adaptive trust region method for unconstrained optimization based on conic model. (English) Zbl 1210.65123
Recently, nonmonotone line search techniques have been studied by many authors. Many authors generalized the nonmonotone technique to trust region methods and proposed nonmonotone trust region methods. Theoretical analysis and numerical results show that the algorithms with nonmonotone properties are more efficient than the usual monotone algorithms.
In this paper a nonmonotone adaptive trust region method for unconstrained optimization based on conic model is presented. A simple way is given to determine the trust region radius at each iterate point. The local and global convergence properties of algorithm are proved under some reasonable assumptions. The numerical results show the efficiency of the new algorithm.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C51 Interior-point methods
Full Text: DOI
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