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Filter Algorithm For Unconstrained Optimization Problems

Posted on:2008-10-29Degree:MasterType:Thesis
Country:ChinaCandidate:R LinFull Text:PDF
GTID:2120360218453027Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In first chapter, we summarize the optimal conditions of unconstrained optimization and its basic model for solving , and summarize a brief history of filter methods, after introducing the investigating significance of the question for discussion and its investigation actuality all over the world. And after offering the common decline algorithm we introduce tow methods of line search. After the confirmation of the decline direction d_k, the searching step-sizeα_k will be confirmed by the line search . At the same time, we briefly make a simple retrospect of SQP algorithm of optimization problems, and by the definitions, we educe the ideas of filter method.In second chapter, we summarize quasi-Newton algorithm. On its generation process, we have made the analysis. Simultaneously we have given the general algorithm step and the convergent results. And we introduce the modified quasi-Newton algorithm. It is used in the condition of nonconvex of objective function on the base of quasi-Newton algorithm, while the choosing of parameter r_k is very important. After a while, we offer a choosing method. By the way, we describe the modified quasi-Newton algorithm used the line search , and have given its global convergence and superlinear convergence.In third chapter, we discussed trust-region algorithm for the unconstrained optimization and elaborate basic structure of this algorithm, and introduce the convergent results of the algorithm briefly. Afterwards, the trust-region algorithm applying SQP is introduced, we simultaneously have also given the convergent results of the algorithm. Finally we introduce the classical SQP filter algorithm as well as its convergent results.And in fourth chapter, we have discuss a unconstrained optimal problem where f : R~n→R is continuously dual-differentiable, when considering accepting x_k +α_kd_k as a new updating point. We construct a new algorithm for unconstrained optimizations. The algorithm combines the idea of MBFGS method with the strategy of multidimensional filter algorithm. One side, the produce of searching direction is similar to MBFGS method; on the other hand, when the new point will be accepted, we adopt the strategy of multidimensional filter algorithm. In addition, the new algorithm has a global convergence. Finally we offer the algorithm's trial of numerical value.
Keywords/Search Tags:unconstrained optimization, line search, filter, quasi-Newton method, MBFGS algorithms, trust-region algorithms, multi-dimension filter
PDF Full Text Request
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