Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory

Trust Region Method for Variational Inequality Problem

Author LiXueZhong
Tutor YinHongYou
School Nanjing University of Aeronautics and Astronautics
Course Computational Mathematics
Keywords Trust region methods Non- monotonic adaptive technology Line search technique Box Constrained Variational Inequality D - gap function
CLC O224
Type Master's thesis
Year 2007
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Trust region methods for solving unconstrained optimization problems more effective method , however, has a great impact of the trust region radius selection algorithm is good or bad . The Zhang Xiangsun given an adaptive trust region algorithm , using the current iteration the point of the gradient and Hessian matrix information to select the current iteration step trust region radius , numerical experiments show that this method is more effective than general trust region methods . In this paper, the currently more popular nonmonotonic the proposed nonmonotone adaptive trust region methods improved , thus reducing the amount of computation . Not heavy when tentative step unacceptable solution to the trust region subproblem nonmonotonic line search techniques . General assumptions , not only there is at least an accumulation point for the stable point , but the improved algorithm point column any accumulation point are the stable point of the original problem . In addition, this improved algorithm remains superlinear convergence . This paper not only linearization but linearized constraint set , the set of constraints for a special class of non-empty closed convex subset of variational inequalities into an equivalent set of constraints for multi- surface convex set line variational inequalities sexual variational inequalities , re-use projection and contraction method of calculation . Box Constrained Variational Inequalities converted into equivalent unconstrained optimization problems , recycling Trust Method .

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