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Combination And Applications Of Filter Technique And Nonmonotone Technique In Numerical Optimization

Posted on:2007-10-21Degree:DoctorType:Dissertation
Country:ChinaCandidate:W H MiaoFull Text:PDF
GTID:1100360185977400Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
The two most important algorithm framework to optimization problem are line search method and trust region method, one of the key constitute parts of them are search direction and trust region subproblem respectively, the other are naturally the framework themselves. In this paper, we focus on improving the framework by introducing some strategy as filter technique and nonmonotone technology, then apply them to a few typical optimization problems. We will both analyse their convergence theories and examine their practical results by numerical experiments.In chapter 2, we mainly consider the application of filter technique to uncon-straint optimization problem, while taking trust region method as basic algorithm framework. Following [39], we use gradient vector to define filter set, while take some improvements on the algorithm framework therein mainly by reducing the judgement to the convexity of trust region subproblem. Then we prove the global convergence of our modified framework, and, under certain condition, give the proof of the convergence to second order critical point. Finally, we show that our filter trust region method is more efficient than classic trust region framework by numerical experiments.In chapter 3, we study the application of nonmonotone technique to nonlinear least square problems, while taking a special line search method-Gauss-Newton method as basic algorithm framework. The theoretical framework of nonmonotone line search technique is given in [41], where some requirements on the search direction were given. In this chapter, we use truncate Gauss-Newton method to satisfy these requirements, and take some improvement on the truncate technology. So, we can prove the convergence theory of our nonmonotone truncate Gauss-Newton method by using the classical result of [41]. At last, we report the corresponding numerical results.In chapter 4, we investigate the application of filter technique to nonlinear equations. As traditional method, we transfer the nonlinear equations to nonlinear least square problem, then solve it by Gauss-Newton method. We also use...
Keywords/Search Tags:filter, nonmonotone, line search, trust region, nonlinear least squares, nonlinear equations, truncate Gauss-Newton method, precondition, iterative refinement, SQP
PDF Full Text Request
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