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A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints |
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| Authors: | Z. -W. Chen J. -Y. Han D. -C. Xu |
| Affiliation: | (1) Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu Province, People's Republic of China wenchen@pub.sz.jsinfo.net , CN;(2) Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China hjyyyf@netease.com , CN;(3) Institute of Computational Mathematics and Scientific$/$Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China xudc@lsec.cc.ac.cn, CN |
| Abstract: | In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient. Accepted 5 September 2000. Online publication 4 December 2000. |
| Keywords: | . Global convergence Nonmonotone Trust region algorithm Non-linear programming Strict complementarity slackness condition. AMS Classification. Primary 65K05 Secondary 90C20. |
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