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A Modified Barzilai And Borwein Scaling Conjugate Gradient Method For Unconstrained Optimization Problems

Posted on:2014-04-25Degree:MasterType:Thesis
Country:ChinaCandidate:L M WangFull Text:PDF
GTID:2250330401969441Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
There are many kinds of iterative methods for solving unconstrained optimiza-tion problems and the most popular methods are the Newton method, quasi-Newton methods, the steepest descent method and conjugate gradient method. The Newton method and quasi-Newton methods are known as the most effective methods, because they have fast rate of convergence property. However, they need to store and compute the matrix associated with Hessian of the objective function, so this produces large computation and storage. And it has negative influence on numerical results. The steepest descent method uses the negative gradient as search directions and only re-quires first-order derivative. But for many problems, the steepest descent method is not the actual "steepest". It descends very slowly with zigzagging phenomena. Gen-erally speaking, the conjugate gradient method is a useful and widely used technique for solving large scale minimization problems because it avoids the computation and storage of some matrices. In addition, the Barzilai and Borwein gradient method has quasi-Newton property and requires less computational work.In this paper, we combine the conjugate gradient method with the Barzilai and Borwein gradient method, and propose a Barzilai and Borwein scaling conjugate gra-dient method for nonlinear unconstrained problems. The new method does not require to compute and store some matrices associated with Hessian of objective functions too. In addition, we have proved the search direction generated by the new algorithm is a descent direction for any inexact line search which fulfills the Wolfe conditions. Moreover, a global convergence result is established when the line search fulfills the Wolfe conditions, and numerical results show that the proposed algorithm is reliable.
Keywords/Search Tags:unconstrained optimization, nonlinear problems, Barzilai and Borweinmethod, conjugate gradient method, global convergence
PDF Full Text Request
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