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# Quasi-newton Method. Family Extended Its Global Convergence,

Posted on:2010-09-25Degree:MasterType:Thesis
Country:ChinaCandidate:W LiuFull Text:PDF
GTID:2190360272494121Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
The Quasi-Newton methods is one of the most effective mothods for solving the unconstrained optimization problems, whose basic idea is to estimate the second order derivatives with the first order derivatives.The main differences between different types of the Quasi-Newton methods are: the change way of estimate of the second order derivatives from one iterate to another iterate, and the types and accuracy of line search. so it produces a series of approximation matrix Bk+1 to the second order derivatives of the objective function. The nature of Bk+1 is Bk+1 = Bk + Ak, in which Bk is the approximation matrix at the last iteration, Ak is some matrix. In this paper, the writer first propose the conditionwhich can satisfy Ak is skTAkskk, in whichθk = 2(fk-fk+1) + skT(gk+1+gk).And then three formulae to satisfy Ak are given: (1)(?); (2)(?); (3)(?), in whichuk,uk∈Rn, and satisfy skTuk≠0,skTuk≠0. From which six reasonable choices are gotten: (1)(?)Based on those choices, the three corresponding algorithms are proved to possess global convergence property. At last eighteen popular test functions have conducted which show that the proposed algorithms are very encouraging.
Keywords/Search Tags:Unconstrained optimization, Quasi-Newton equation, Global convergence
PDF Full Text Request
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