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Parallel BFGS Algorithm For A Class Of Large Scale Optimization Problem

Posted on:2007-10-23Degree:MasterType:Thesis
Country:ChinaCandidate:X G WuFull Text:PDF
GTID:2120360185965748Subject:Probability theory and mathematical statistics
Abstract/Summary:PDF Full Text Request
Quasi-Newton methods are welcome numerical methods for solving optimization problems. They are particularly effective when applied to solve small or middle size problems. BFGS method is regarded as the most effective quasi-Newton method due to its good numerical performance. It also possesses very good global and superlinear convergence properties. On the other hand, however, when applied to solve large scale problems, quasi-Newton methods including BFGS method do not perform well. The major drawback for a quasi-Newton method, when used to solve large scale optimization problem, is that the matrix generated by the method does not retain the sparsity of the Hessian matrix of the objective function. There are examples showing that many successful methods for solving small-sized optimization become unattractive once the problem to be tackled is large. An important reason for this feature is that some process that is unimportant for small problems may become very expensive for large scale problems.The fast development of computer has enhanced our ability to solve large scale problems. In particular, the parallel computer provides us a new way to solve large scale problems efficiently. In recent years, there has been growing interest in the study in parallel methods. It has been found that many good methods that are efficient for solving small and middle size problems can be parallized. Numerical results show that this kind of parallel method works well.The purpose of this thesis is devoted to parallel BFGS method. On the basis of the Broyden's rank one method for solving systems of nonlinear equations, we develop a parallel BFGS method for solving a class of large scale optimization problems. We split the problem into several small sub-problems with overlap variables. At each step, we solve these sub- problems parallelly by BFGS method. Under appropriate conditions, we prove the local convergence property of the algorithm.
Keywords/Search Tags:BFGS quasi-Newton method, overlap, unconstrained optimization problem, large scale problem
PDF Full Text Request
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