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Quasi-newton Equation Based On The Fourth-order Trust Region Algorithm

Posted on:2013-01-22Degree:MasterType:Thesis
Country:ChinaCandidate:X M WangFull Text:PDF
GTID:2210330374463498Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Quasi-Newton algorithm is the promotion of the Newton method. It needsmuch of work in each iteration of using the Newton method to calculate theHessian matrix. By using Newton method and it is not easy or even difficult tocalculate the Hessian matrix. In order to overcome this disadvantage of Newtonmethod, the researchers constructed a method named quasi-Newton algorithmbased on quasi-Newton equation. By using the information of the first derivativeof the objective function, quasi-Newton constructs the approximate curvature ofthe objective function. This algorithm don't need to calculate to the Hessianmatrix and has super linear convergence.The quasi-Newton algorithm plays a crucial role in unconstrainedoptimization process. Traditional quasi-Newton equation ignores theinformation of the objective function value; it only uses its gradient information,it is a great waste of information resources. Taking the full use of informationresources into account, at present many researchers modified the traditionalquasi-Newton equation and proposed a new quasi-Newton algorithm. In thispaper, combining with the trust region algorithm, line search technologies, takesa research on the second model and cone model based on the literature [7] inwhich put forward four-order quasi-Newton equation. These mixed algorithmbasing on the quasi-Newton algorithm not only retain the majority properties ofthe old quasi-Newton algorithm, but also can be more exact than the old one inquadratic curvature approximate of the objective function. The main contentsof this paper are as follows:Firstly, on the basis of the new quasi-Newton equation with four order anda BFGS corrector formula, we introduce a concept of self-adapt. According toArmijo line search technique, a new non-monotonic trust region algorithm isproposed. In the paper, the convergence of the algorithm is proved in certaincondition, and the relevant numerical result is given at the same time.Secondly, on the basis of the new quasi-Newton equation with four order and a BFGS corrector formula, we propose a quasi-Newton non-monotonic trustregion algorithm combining both the non-monotonic Wolfe line searchtechnique and trust region method about the new cone model. In lowercondition, we prove that the new algorithm is convergence. And the numericalresult shows the algorithm is effective.Thirdly, on the basis of the new quasi-Newton equation with four order anda BFGS corrector formula, we propose a non-monotonic trust region algorithmabout the new cone model, and the convergence of the algorithm in certaincondition is proved, and the relevant numerical result is given at the same time.
Keywords/Search Tags:Unconstrained optimization, Quasi-Newton equation, Quasi-Newton method, Global convergence
PDF Full Text Request
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