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Zbl 0797.90088
Deng, N.Y.; Xiao, Y.; Zhou, F.J.
Nonmonotonic trust region algorithm. (English)
[J] J. Optimization Theory Appl. 76, No.2, 259-285 (1993). ISSN 0022-3239; ISSN 1573-2878/e

Summary: A nonmonotonic trust region method for unconstrained optimization problems is presented. Although the method allows the sequence of values of the objective function to be nonmonotonic, convergence properties similar to those for the usual trust region method are proved under certain conditions, including conditions on the approximate solutions to the subproblem. To make the solution satisfy these conditions, an algorithm to solve the subproblem is also established. Finally, some numerical results are reported which show that the non-monotonic trust region method is superior to the usual trust region method according to both the number of gradient evaluations and the number of function evaluations.

MSC 2000:: *90C30 Nonlinear programming
90-08 Computational methods (optimization)

Keywords: nonmontonic trust region method; unconstrained optimization

Cited in: Zbl 1052.90615

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