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Nomonotone Trust Region Algorithms for Unconstrained Optimization

Author: RenQin
Tutor: DongYunDa
School: Zhengzhou University
Course: Operational Research and Cybernetics
Keywords: Trust region method Nonmonotonicity Convergence
CLC: O224
Type: Master's thesis
Year: 2008
Downloads: 20
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Abstract


Nonmonotonic trust region methods nonmonotonic trust region method does not require the function value at every step of the decline , it is a good convergence of the algorithm . Strong convergence and better numerical performance nonmonotonic trust region methods for unconstrained optimization problems an important class of numerical methods in recent years by the optimization of the attention of the research community . Brief Chapter the basic theory of the trust region method , research progress and research significance . gives a solution of unconstrained optimization problems nonmonotonic trust region BFGS correction algorithm . The non- monotonic algorithm is applied to the solution of the trust region problem . The key is to put forward the the new BFGS correction formula , this algorithm has a good nature , trust region subproblem given the BFGS correction with quadratic constraints always ensure correction matrix is positive definite , and that the trust region subproblem strictly convex quadratic programming . Proved that the algorithm has global convergence in fewer assumptions related theory . Third chapter gives an improved constraint optimization nonmonotone trust region algorithms to improve the general non - monotonic algorithm range . iterative speed , in this chapter with respect to the traditional method lt in r_k ; 0 amplified ( ?) so you can faster iteration to r_k gt ; 0 , lessening the overall constraints of the algorithm . text global convergence and superlinear convergence rate . [ 20 ] algorithm proved ( ? ) to set up the conditions under this chapter to remove this constraint conditions still obtain the global convergence of the algorithm and its superlinear convergence rate , so as to promote nonmonotonic trust region method range of applications Chapter decomposition based on symmetric matrices Bunch-Parlett , will be converted into an equivalent of the trust region subproblem trust region subproblem , and construct a gradient path is easy to implement , then along this path with nonmonotonic trust region method to find the problem about the optimal solution , no definite limit the law of the sea color matrix , retains the characteristics of the trust region methods , and prove the algorithm 's global convergence and second - order rate of convergence Chapter [17] proposed trust region subproblem nonmonotonic technology combine to produce a non- monotonic adaptive trust region algorithm , and prove the global convergence of the algorithm .

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