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A Quasi-Newton Trust Region Algorithm with the New Conic Model

Author: LuJianYan
Tutor: NiQin
School: Nanjing University of Aeronautics and Astronautics
Course: Operational Research and Cybernetics
Keywords: Unconstrained Optimization Cone model Quadratic model Trust region method Cone model sub-problems
CLC: O221.2
Type: Master's thesis
Year: 2009
Downloads: 18
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Abstract


Traditional optimization methods are generally used quadratic model to approximate the original problem . Davidon in 1980 first proposed a quadratic function more than cone function in general, have more freedom to make fuller use of the previous iteration function information . Currently cone model for solving trust region subproblem approximation method are generally put it into a quadratic model , and then by using a quadratic model transformation method to solve the quadratic model , and finally draw a corresponding domain Conic Trust sub- optimal solution , but in the approximation of the transformation process may lose some of the features cone function . Therefore, this paper studies a new solution cone model trust region subproblem new method which does not require the cone model into sub-problems to solve quadratic model , but directly on the cone model sub-problem is solved . The idea of ??the method comes from the solution of quadratic model trust region subproblem More classical methods . In this chapter , we introduce the quadratic model based on traditional overview of trust region method , in which a special presentation on child problem solving quadratic model More classical methods . In the second chapter, we introduce the concept of cone function and some properties , and to propose new conic model trust region subproblem structure and its parameters . The third chapter is the most distinctive part of this article , we propose a model to understand the new conic trust region subproblem new algorithm to analyze the basic idea of the algorithm and prove that the new method of sub-problems approximate solution and the optimal solution is estimated Nature . In the fourth chapter, we propose a new algorithm for sub-problems based on a complete new conic model trust region algorithm and its global convergence . In the fifth chapter, we have proposed a new conic model trust region methods for numerical experimental results show that the proposed algorithm may be a new class of effective algorithms.

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming) > Nonlinear Programming
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