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Algorithm for Solving Subspace Trust-region Subproblem with Conic Model

Author: ZhangXin
Tutor: NiQin
School: Nanjing University of Aeronautics and Astronautics
Course: Operational Research and Cybernetics
Keywords: Unconstrained optimization subspace technique conic model quadratic model trust region method global convergence
CLC: O221.2
Type: Master's thesis
Year: 2009
Downloads: 6
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Abstract


The subspace techniques are getting more and more important as the optimization problems are getting larger and larger in scale. The applications of subspace techniques have the advantage of reducing both computation cost and memory size. On the other hand, trust region method has attracted more attention for recent years because of its remarkable numerical reliability and strong convergent theory. And it has been widely used into many optimization problems. However, traditional trust region method usually based upon modeling the function locally by a quadratic function. Thus if the objective function has strong non-quadratic behavior or its curvature changes severely, the quadratic model methods often produce a poor prediction of the minimization of the function while the conic model one may serve better. That’s because the conic model is a generalization of the quadratic model and can take into account more information from previous iterations. During the past twenty years, the trust region method based on conic model has attracted the attention of more and more researchers.This paper applies subspace technique to trust-region subproblem involving a conic model, and proposes subspace trust-region subproblem with conic model and solves it using dogleg method. The dissertation consists of four chapters. Chapter 1 is introductory. The purposes, significance, contents and its research status of this dissertation are discussed. Chapter2 contains some preparatory materials of trust region method, the conic model and subspace technique. Chapters 3 and 4 are our main contribution. In chapter 3, we first convert subspace trust-region subproblem with conic model into a lower dimension case, then solve it using dogleg method and return the solution to the previous problem. Moreover, we have proved the decreasing property of this algorithm. In Chapter 4 we solve the unconstrained optimization problem by the result got in chapter 2, and propose the subspace conic model trust-region algorithm and prove its global convergence. Finally, in Chapter 5, numerical experiment results are given. The numerical experiment results show that the subspace trust-region algorithm with conic model is efficient and promising.

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