Filter Trust Region Algorithms For Unconstrained Optimization

In this paper we present filter trust region algorithms for solving unconstrained op-timization problems. Fletcher and Leyfer proposed a filter method in1997to get overnumerical difculty when using improper penalty function for nonlinear constrainedoptimization problems. Filter technology has been widely applied to other optimiza-tion fields, due to its good convergence properties and numerical results. Such assolving nonlinear equations and unconstrained optimization problems,ones have pro-posed many efective algorithms based on filter technology. However, the efect of thesealgorithms greatly depend on the filter rules. In this paper we make further study thefilter structure and the relevant rules and then present two kinds of filter trust regionalgorithms: Cautious filter trust region algorithm and filter trust region algorithm withfour parameters.In Chapter1, we mainly introduce the development of the filter algorithm, do-mestic and international current situation analysis and its research significance of filteralgorithm. We introduces also the general trust region algorithm structure, definitionof general multidimensional filter and filter trust region algorithm.In Chapter2, we propose the definition of Cautious filter, which is a modificationof traditional filter, has reduced some flaws in the existing filter structure, such as somedifculties in the choice of parameter caused by the rigid filter rules. Meanwhile, weproposed the global convergence of cautious filter.In Chapter3, we present the filter trust region algorithm with four parameters,which is an extension of the filter trust region algorithm with two parameters. Thefilter technology with four parameters is more flexible for the choice of parameters andthe form is more diversified, and the filter technology with two parameters is a specialform of that. Therefore, it contains the advantage of the filter trust region algorithmwith two parameters. At last we prove the global and superlinear convergence of theproposed algorithm.In Chapter4, we perform the proposed algorithms. The numerical results showthat the proposed algorithms are practical efcient.