Font Size: a A A

A Class Of The Preconvex Part Of Modified Broyden's Family For Solving Unconstrained Optimization Problem

Posted on:2007-02-25Degree:MasterType:Thesis
Country:ChinaCandidate:P J XieFull Text:PDF
GTID:2120360185987466Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
We mainly research the application of a class of the preconvex part of modified Broy-den's family, which are geanerated from a new quasi-Newton equations, to unconstrained optimization. The thesis is organized as follows:In Chapter 1, we review the basic thought and research of the Broyden's family algorithms. Wei at al.(2004) proposed a class of the new quasi-Newton equations Bk+1Sk = yk* = yk + AkSk, where Ak is some matrix, based on this we give two type of modified Broyden's family (MBC1,MBC2) and analyse the correspending properties.In Chapter 2, combining two types of the preconvex part of modified Broyden's family with Armijo line search, we get two algorithms for solving unconstrained optimization problems, and prove these algorithms are global and superlinear convergence under some suitable conditions.In Chapter 3, we propose two new quasi-Newton type trust region methods for solving unconstrained optimization problems. These algorithms combine two types of the preconvex part of modified Broyden's family proposed in chapter 1 with trust region algorithm effectively, they have global convergence property and superlinear convergence rate.
Keywords/Search Tags:unconstrained optimization problems, preconvex part of Broyden's family, trust region method, global convergence, superlinear convergence
PDF Full Text Request
Related items