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Nonmonotonic trust region algorithm. (English) Zbl 0797.90088
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.

90C30Nonlinear programming
90-08Computational methods (optimization)
Full Text: DOI
[1] Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., andPedersen, H. C.,The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization, Mathematical Programming Study, Vol. 26, pp. 1-17, 1986. · Zbl 0477.90072
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[7] Sorensen, D. C.,Newton’s Method with a Model Trust Region Modification, SIAM Journal on Numerical Analysis, Vol. 19, pp. 409-426, 1982. · Zbl 0483.65039 · doi:10.1137/0719026
[8] Steihaug, T.,The Conjugate Gradient Method and Trust Regions in Large-Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, pp. 626-637, 1983. · Zbl 0518.65042 · doi:10.1137/0720042
[9] Dennis, J. E., Jr., andMei, H. H. W.,Two New Unconstrained Optimization Algorithms Which Use Function and Gradient Values, Journal of Optimization Theory and Applications, Vol. 28, pp. 453-482, 1979. · Zbl 0388.65022 · doi:10.1007/BF00932218
[10] Dennis, J. E., Jr., andSchnabel, R. B.,Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983.