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D. W. Marquardt, “An Algorithm for Least Squares Estimation of Nonlinear Inequalities,” SIAM Journal on Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431-441.

has been cited by the following article:

• TITLE: A Retrospective Filter Trust Region Algorithm for Unconstrained Optimization

  AUTHORS: Yue Lu, Zhongwen Chen

  KEYWORDS: Unconstrained Optimization, Retrospective, Trust Region Method, Multi-Dimensional Filter Technique

  JOURNAL NAME: Applied Mathematics, Vol.1 No.3, September 29, 2010

  ABSTRACT: In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi-dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step for the usual trust region methods. Under reasonable assumptions, we analyze the global convergence of the new method and report the preliminary results of numerical tests. We compare the results with those of the basic trust region algorithm, the filter trust region algorithm and the retrospective trust region algorithm, which shows the effectiveness of the new algorithm.