An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

Liu, Jianjun; Xu, Xiangmin; Cui, Xuehui

doi:10.1007/s10589-017-9941-6

Cited by 7 publications

(1 citation statement)

References 17 publications

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“…This class of problems often arises in a wide variety of science, engineering and environment such as medical and biomedical imaging problems (Oeuvray 2005;Oeuvray and Bierlaire 2007) and groundwater problem (Fowler et al 2008). Trust-region methods constitute a prominent class of iterative methods for solving unconstrained optimization problems (Saeidian et al 2017;Ferreira et al 2015;Fu and Sun 2005;Liu et al 2018). In these techniques, the objective function is approximated by a model, and this model is minimized in a neighborhood of the current iterate.…”

Section: Introductionmentioning

confidence: 99%

An improved hybrid-ORBIT algorithm based on point sorting and MLE technique

et al. 2019

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Optimization using radial basis functions as an interpolation tool in trust region (ORBIT) is a derivative-free framework based on fully linear radial basis function (RBF) models. In this paper, an improved version of ORBIT algorithm based on two novel ideas is proposed. The accuracy and stability of RBFs depend on a so-called shape parameter, so it is more appropriate to determine the shape parameter according to the optimization problem. While ORBIT in all problems uses a fixed value as a shape parameter, our new version, Hybrid-ORBIT, uses a statistical technique to select an appropriate shape parameter. In addition, ORBIT uses some stored points to build a fully linear RBF model without considering their function values, while in the Hybrid-ORBIT algorithm the stored points are sorted based on their function values and the RBF model is built using the points with lower function values, and the best point in the sense of function value is defined as the trust-region center. Numerical results indicate the efficiency of the improved version compared with the original version.

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